Handbook of Nonlinear Partial Differential Equations, Second Edition

Information > Mathematical Books > Handbook of Nonlinear Partial Differential Equations, Second Edition > References

A. D. Polyanin and V. F. Zaitsev

Handbook of Nonlinear Partial Differential Equations
Second Edition, Updated, Revised and Extended

Publisher: Chapman & Hall/CRC Press, Boca Raton-London-New York
Year of Publication: 2012
Number of Pages: 1912

Summary Preface Features Contents References Index (pdf 117K)

References

Abbot, T. N. J. and Walters, K., Rheometrical flow systems. Part 2. Theory for the orthogonal rheometer, including an exact solution of the Navier–Stokes equations, Fluid Mech., Vol. 40, pp. 205–213, 1970.
Abel, M. L. and Braselton, J. P., Maple by Example, 3rd ed., AP Professional, Boston, MA, 2005.
Ablowitz, M. J. and Clarkson, P. A., Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge Univ. Press, Cambridge, 1991.
Ablowitz, M. J., Kaup, D. J., Newell, A. C., and Segur, H., The inverse scattering transform–Fourier analysis for nonlinear problems, Stud. Appl. Math., Vol. 53, pp. 249–315, 1974.
Ablowitz, M. J., Ramany, A., and Segur, H., A connection between nonlinear evolution equations and ordinary differential equations of P-type, J. Math. Phys., Vol. 21, pp. 715–721, 1980.
Ablowitz, M. J. and Segur, H., Solitons and the Inverse Scattering Transform, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1981.
Ablowitz, M. J. and Zeppetella, A., Explicit solutions of Fisher's equation for a special wave speed, Bull. Math. Biology, Vol. 41, pp. 835–840, 1979.
Abramenko, A. A., Lagno, V. I., and Samoilenko, A. M., Group classification of nonlinear evolutionary equations. I. Invariance under semisimple groups of local transformations [in Russian], Diff. Uravneniya, Vol. 38, No. 3, pp. 365–372, 2002.
Abramenko, A. A., Lagno, V. I., and Samoilenko, A. M., Group classification of nonlinear evolutionary equations. II. Invariance under solvable groups of local transformations [in Russian], Diff. Uravneniya, Vol. 38, No. 4, pp. 482–489, 2002.
Abramowitz, M. and Stegun, I. A. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards Applied Mathematics, Washington, 1964.
Aczel, J., Functional Equations: History, Applications and Theory, Kluwer Academic, Dordrecht, 2002.
Aczel, J., Lectures on Functional Equations and Their Applications, Dover Publications, New York, 2006.
Aczel, J. and Dhombres, J., Functional Equations in Several Variables, Cambridge University Press, Cambridge, 1989.
Adler, V., Shabat, A. B., and Yamilov, R. I., Symmetry approach to the integrability problems, Theor. Math. Phys., Vol. 125, No. 3, pp. 1603–1661, 2000.
Agrawal, H. L., A new exact solution of the equations of viscous motion with axial symmetry, Quart. J. Mech. Appl. Math., Vol. 10, pp. 42–44, 1957.
Akhatov, I. Sh., Gazizov, R. K., and Ibragimov, N. H., Nonlocal symmetries. Heuristic approach [in Russian], In: Itogi Nauki i Tekhniki, Ser. Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 34, VINITI, Moscow, 1989 (English translation in J. Soviet Math., Vol. 55(1), p. 1401, 1991).
Akhmediev, N. N. and Ankiewicz, A., Solitons. Nonlinear Pulses and Beams, Chapman & Hall, London, 1997.
Akritas, A. G., Elements of Computer Algebra with Applications, Wiley, New York, 1989.
Akulenko, L. D., Georgievskii, D. V., and Kumakshev, S. A., Solutions of the Jeffery–Hamel problem regularly extendable in the Reynolds number, Fluid Dynamics, Vol. 39, No. 1, pp. 12–28, 2004.
Akulenko, L. D. and Kumakshev, S. A., Multimode bifurcation of the flow of a viscous fluid in a plane diffuser, Doklady Physics, Vol. 49, No. 12, pp. 620–624, 2004.
Akulenko, L. D., Kumakshev, S. A., and Nesterov, S. V., Effective numerical–analytical solution of isoperimetric variational problems of mechanics by an accelerated convergence method, J. Appl. Math. Mech. (PMM), Vol. 66, No. 5, pp. 693–708, 2002.
Amerov, T. K., On conditional invariance of nonlinear heat equation, In: Theoretical and Algebraic Analysis of Equations of Mathematical Physics, Inst. of Mathematics, Kiev, pp. 12–14, 1990.
Ames, W. F., Nonlinear Partial Differential Equations in Engineering, Vol. 1, Academic Press, New York, 1967.
Ames, W. F., Nonlinear Partial Differential Equations in Engineering, Vol. 2, Academic Press, New York, 1972.
Ames, W. F., Lohner, J. R., and Adams E., Group properties of u_tt = [f(u)u_x]_x, Int. J. Nonlinear Mech., Vol. 16, No. 5–6, p. 439, 1981.
Anderson, R. L. and Ibragimov, N. H., Lie–Backlund Transformations in Applications, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1979.
Andreev, V. K., Stability of Unsteady Motions of a Fluid with a Free Boundary [in Russian], Nauka, Novosibirsk, 1992.
Andreev, V. K., Kaptsov, O. V., Pukhnachov, V. V., and Rodionov, A. A., Applications of Group-Theoretical Methods in Hydrodynamics, Kluwer, Dordrecht, 1998.
Andreyanov, B. P., Vanishing viscosity method and an explicit solution of the Riemann problem with the scalar conservation law, Moscow Univ. Math. Bulletin, No. 1, pp. 3–8, 1999.
Annin, B. D., One exact solution of an axisymmetric problem of ideal plasticity, Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki [in Russian], Vol. 2, p. 171, 1973.
Annin, B. D., Modern Models of Plastic Bodies [in Russian], Novosibirsk State University, Novosibirsk, 1975.
Annin, B. D., Bytev, V. O., and Senashov, S. I., Group Properties of Equations of Elasticity and Plasticity [in Russian], Nauka, Novosibirsk, 1985.
Aoki, H., Higher-order calculation of finite periodic standing waves by means of the computer, J. Phys. Soc. Jpn., Vol. 49, pp. 1598–1606, 1980.
Appell, P., Traite de Mecanique Rationnelle, T. 1: Statique. Dinamyque du Point (Ed. 6), Gauthier-Villars, Paris, 1953.
Aristov, S. N., An exact solution to the point-source problem, Doklady Physics, Vol. 40, No. 7, pp. 346–348, 1995.
Aristov, S. N., Three-dimensional conical viscous incompressible fluid flows, Fluid Dynamics, Vol. 33, No. 6, pp. 929–932, 1998.
Aristov, S. N., Exact periodic and localized solutions of the equation h_t =Δ lnh, J. Appl. Mech. & Tech. Phys., Vol. 40, No. 1, pp. 16–19, 1999.
Aristov, S. N., A stationary cylindrical vortex in a viscous fluid, Doklady Physics, Vol. 46, No. 4, pp. 251–253, 2001.
Aristov, S. N. and Gitman, I. M., Viscous flow between two moving parallel disks: exact solutions and stability analysis, J. Fluid Mech., Vol. 464, pp. 209–215, 2002.
Aristov, S. N. and Knyazev, D. V., New exact solution of the problem of rotationally symmetric Couette–Poiseuille flow, J. Appl. Mech. Tech. Phys., Vol. 48, No. 5, pp. 680–685, 2007.
Aristov, S. N. and Knyazev, D. V., Localized helically symmetric flows of an ideal fluid, J. Appl. Mech. Tech. Phys., Vol. 51, No. 6, pp. 815–818, 2010.
Aristov, S. N., Knyazev, D. V., and Polyanin, A. D., Exact solutions of the Navier–Stokes equations with the linear dependence of velocity components of two space variables, Theor. Foundations of Chemical Engineering, Vol. 43, No. 5, pp. 642–662, 2009.
Aristov, S. N. and Polyanin, A. D., Exact solutions of unsteady three-dimensional Navier–Stokes equations, Doklady Physics, Vol. 54, No. 7, pp. 316–321, 2009.
Aristov, S. N. and Polyanin, A. D., New classes of exact solutions and some transformations of the Navier–Stokes equations, Russian J. of Math. Physics, Vol. 17, No. 1, pp. 1–18, 2010.
Aristov, S. N. and Pukhnachev, V. V., On the equations of axisymmetric motion of a viscous incompressible fluid, Doklady Physics, Vol. 49, No. 2, pp. 112–115, 2004.
Arnold, V. I., Mathematical Methods of Classical Mechanics, Springer-Verlag, New York, 1980.
Arnold, V. I., Arnold's Problems [in Russian], Fazis, Moscow, 2000 [English Edition, Springer, 2005].
Arrigo, D., Broadbridge, P., and Hill, J. M., Nonclassical symmetry solutions and the methods of Bluman–Cole and Clarkson–Kruskal, J. Math. Phys., Vol. 34, pp. 4692–4703, 1993.
Ashwell, D. G., Quart. J. Mech. Appl. Math., Vol. 10, p. 169, 1957.
Astafiev, V. I., Radayev, Yu. N., and Stepanova, L. V., Nonlinear Fracture Mechanics [in Russian], Samarsky University Publ., Samara, 2001.
Babich, V. M., Kapilevich, M. B., Mikhlin, S. G., et al., Linear Equations of Mathematical Physics [in Russian], Nauka, Moscow, 1964.
Bahder, T. B., Mathematica for Scientists and Engineers, Addison-Wesley, Redwood City, CA, 1995.
Baidulov, V. G., Nonlinear dynamics of internal waves within the framework of a one-dimensional model, Doklady Physics, Vol. 55, No. 6, pp. 302–307, 2010.
Baikov, V. A., Approximate group analysis of nonlinear models of continuum mechanics, Ph.D. thesis [in Russian], Keldysh Institute of Applied Mathematics, Moscow, 1990.
Baikov, V. A., Gazizov, R. K., and Ibragimov, N. H., Perturbation methods in group analysis [in Russian], in: Contemporary Problems of Mathematics, Vol. 34 (Itogi Nauki i Tekhniki, VINITI AN USSR), Moscow, pp. 85–147, 1989.
Bakirova, M. I., Dimova, S. N., Dorodnitsyn, V. A., Kurdyumov, S. P., Samarskii, A. A., and Svirshchevskii, S. R., Invariant solutions of heat equation describing the directed propagation of combustion and spiral waves in nonlinear medium [in Russian], Dokl. Acad. Nauk USSR, Vol. 299, No. 2, pp. 346–350, 1988.
Barannyk, T., Symmetry and exact solutions for systems of nonlinear reaction-diffusion equations, Proc. of Inst. of Mathematics of NAS of Ukraine, Vol. 43, Part 1, pp. 80–85, 2002.
Barannyk, T. A. and Nikitin, A. G., Solitary wave solutions for heat equations, Proc. of Inst. of Mathematics of NAS of Ukraine, Vol. 50, Part 1, pp. 34–39, 2004.
Barbashev, B. M. and Chernikov, N. A., Solution and quantization of a nonlinear two-dimensional Born–Infeld type model [in Russian], Zhurn. Eksper. i Teor. Fiziki, Vol. 50, No. 5, pp. 1296–1308, 1966.
Bardi, M. and Dolcetta, I. C., Optimal Control and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations, Birkhauser, Boston, 1998.
Barenblatt, G. I., On nonsteady motions of gas and fluid in porous medium, Appl. Math. and Mech. (PMM), Vol. 16, No. 1, pp. 67–78, 1952.
Barenblatt, G. I., Dimensional Analysis, Gordon Breach, New York, 1989.
Barenblatt, G. I. and Chernyi, G. G., On moment relations on surface of discontinuity in dissipative media, J. Appl. Math. Mech. (PMM), Vol. 27, No. 5, pp. 1205–1218, 1963.
Barenblatt, G. I., Entov, V. M., and Ryzhik, V. M., Theory of Fluid Flows Through Natural Rocks, Kluwer, Dordrecht, 1991.
Barenblatt, G. I. and Zel'dovich, Ya. B., On dipole-type solutions in problems of nonstationary filtration of gas under polytropic regime [in Russian], Prikl. Math. Mech. (PMM), Vol. 21, pp. 718–720, 1957.
Barenblatt, G. I. and Zel'dovich, Ya. B., Self-similar solutions as intermediate asymptotics, Annual Rev. of Fluid Mech., Vol. 4, pp. 285–312, 1972.
Barron, E. N. and Jensen, R., Generalized viscosity solutions for Hamilton–Jacobi equations with time-measurable Hamiltonians, J. Different. Equations, Vol. 68, No. 1, pp. 10–21, 1987.
Batchelor, G. K., Note on class of solutions of the Navier–Stokes equations representing steady rotationally-symmetric flow, Quart. J. Mech. Appl. Math., Vol. 4, pp. 29–41, 1951.
Batchelor, G. K., An Introduction of Fluid Dynamics, Cambridge Univ. Press, Cambridge, 1970.
Baumann, G., Symmetry Analysis of Differential Equations with Mathematica, Springer-Verlag, New York, 2000.
Beals, R., Sattinger, D. H., and Szmigielski, J., Inverse scattering solutions of the Hunter–Saxton equation, Applicable Analysis, Vol. 78, No. 3–4, pp. 255–269, 2001.
Becker, E., Laminar film flow on a cylindrical surface, J. Fluid Mech., Vol. 74, pp. 297–315, 1976.
Bedrikovetsky, P. G., Mathematical Theory of Oil and Gas Recovery, Kluwer, Dordrecht, 1993.
Bedrikovetsky P. Systems of First-Order Equations Describing Convective Mass Transfer with Volume Reaction, In: Handbook of Mathematics for Engineers and Scientists (by Polyanin A. D., Manzhirov A. V.), pp. 779–780. Boca Raton–London: Chapman Hall/CRC Press, 2007.
Bedrikovetsky, P. G. and Chumak, M.L., Exact solutions for two-phase multicomponent flow in porous media [in Russian], Doklady AN USSR, Vol. 322, No. 4, pp. 668–673, 1992.
Bedrikovetsky, P. G. and Chumak, M.L., Riemann problem for two-phase four and more component displacement (ideal mixtures), Proc. 3rd European Conference on the Mathematics in Oil Recovery, Delft, Holland, pp. 139–148, 1992.
Bekir, A., Application of the G'/G-expansion method for nonlinear evolution equations, Phys. Lett. A, Vol. 372, pp. 3400–3406, 2008.
Bellamy-Knights, P. G., Unsteady multicellular viscous vortices, J. Fluid Mech., Vol. 50, pp. 1–16, 1971.
Bellman, R., Dynamic Programming, Princeton Univ. Press, Pricenton, NJ, 1957.
Belokolos, E. D., General formulae for solutions of initial and boundary value problems for sine-Gordon equation, Theor. Math. Phys., 1995, Vol. 103, No. 3, pp. 613–620.
Belokolos, E. D., Bobenko, A. I., Enol'skii, V. Z., Its, A. R., and Matveev, V. B., Algebro-Geometric Approach to Nonlinear Integrable Equations, Springer, Berlin, 1994.
Belotserkovskii, O. M. and Oparin, A. M., Numerical Experiment in Turbulence [in Russian], Nauka, Moscow, 2000.
Benjamin, T. B., Bona, J. L., and Mahony, J. J., Model equation for long waves in nonlinear dispersive systems, Philos. Trans. Roy. Soc. London, Vol. 272A, pp. 47–78, 1972.
Benton, E. R. and Platzman, G. W., A table of solutions of the one-dimensional Burgers equation, Quart. Appl. Math., Vol. 30, pp. 195–212, 1972.
Berezkin, E. N., Lectures on Theoretical Mechanics [in Russian], Izd-vo Moskovskogo Universiteta, Moscow, 1968.
Berker, R., Integration des equations du mouvement d'un fluide visqueux incompressible, In: Encyclopedia of Physics, Vol. VIII/2 (Ed. S. Flugge), pp. 1–384, Springer-Verlag, Berlin, 1963.
Berker, R., A new solution of the Navier–Stokes equations for the motion of a fluid contained between parallel plates rotating about the same axis, Arch. Mech. Stosow, Vol. 31, No. 2, pp. 265–280, 1979.
Berker, R., An exact solution of the Navier–Stokes equation: the vortex with curvilinear axis, Int. J. Eng. Sci., Vol. 20, No. 2, pp. 217–230, 1982.
Berman, A. S., Laminar flow in channels with porous walls, J. Appl. Physics, Vol. 24, No. 9, pp. 1232–1235, 1953.
Berman, A. S., Effects of porous boundaries on the flow of fluids in systems with various geometries, Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy, Vol. 4, Geneva: UN, pp. 353–358, 1958.
Berman, V. S., Group properties of a hyperbolic system of two differential equations encountered in the theory of mass transfer, Fluid Dynamics, Vol. 16, No. 3, pp. 367–373, 1981.
Berman, V. S. and Danilov, Yu. A., On group properties of the generalized Landau–Ginzburg solution [in Russian], Doklady AN USSR, Vol. 258, No. 1, pp. 67–70, 1981.
Berman, V. S., Galin, L. A., and Churmaev, O. M., Analysis of a simple model of a bubble-liquid reactor, Fluid Dynamics, Vol. 14, No. 5, pp. 740–747, 1979.
Bertozzi, A. L. and Pugh, M., The lubrication approximations for thin viscous films: regularity and long time behaviour of weak solutions, Commun. Pure Appl. Math., Vol. 49, pp. 85–123, 1996.
Bertsch, M., Kersner, R., and Peletier, L. A., Positivity versus localization in degenerate diffusion equations, Nonlinear Analys., Theory, Meth. and Appl., Vol. 9, No. 9, pp. 987–1008, 1985.
Bespalov, V. I. and Pasmannik, G. A., Nonlinear Optics and Adaptive Laser Systems [in Russian], Nauka, Moscow, 1986.
Beutler, R., Positon solutions of the sine-Gordon equation, J. Math. Phys., Vol. 34, pp. 3098–3109, 1993.
Bickley, W., The plane jet, Phil. Mag., Ser. 7, Vol. 23, pp. 727–731, 1939.
Bikbaev, R. F., Shock waves in the modified Korteweg–de Vries–Burgers equation, J. Nonlinear Sci., Vol. 5, pp. 1–10, 1995.
Bird, R. B. and Curtiss, C. F., Tangential Newtonian flow in annuli. 1. Unsteady state velocity profiles, Chem. Eng. Sci., Vol. 11, No. 2, pp. 108–113, 1959.
Birkhoff, G., Hydrodynamics, Princeton University Press, Princeton, NJ, 1950.
Blasius, H., Crenzschichten in Flussigkeiten mit Kleiner Reibung, Zeitschr. fur Math. und Phys., Bd. 56, Ht. 1, S. 1–37, 1908.
Bluman, G. W. and Cole, J. D., The general similarity solution of the heat equation, J. Math. Mech., Vol. 18, pp. 1025–1042, 1969.
Bluman, G. W. and Cole, J. D., Similarity Methods for Differential Equations, Springer-Verlag, New York, 1974.
Bluman, G. W. and Kumei, S., On the remarkable nonlinear diffusion equation [a (u+b)^-2u_x]_x− u_t=0, J. Math. Phys., Vol. 21, No. 5, pp. 1019–1023, 1980.
Bluman, G. W. and Kumei, S., Symmetries and Differential Equations, Springer-Verlag, New York, 1989.
Blyth, M. G. and Hall, P., Oscillatory flow near a stagnation point, SIAM J. Appl. Math., Vol. 63, pp. 1604–1614, 2003.
Blyth, M. G., Hall, P., and Parageorgiu, D. T., Chaotic flows in pulsating cylindrical tubes: a class of exact Navier–Stokes solutions, J. Fluid Mech., Vol. 481, pp. 187–213, 2003.
Bodewadt, U. T., Die Drehstromung uber festem Grunde, ZAMM, Vol. 20, pp. 241–253, 1940.
Bodonyi, R. J. and Stewartson, K., The unsteady laminar boundary layer on a rotating disk in a counter-rotating fluid, J. Fluid Mech., Vol. 79, pp. 669–688, 1977.
Bogdanov, L. V. and Zakharov, V. E., The Boussinesq equation revisited, Phys. D., Vol. 165, pp. 137–162, 2002.
Bogoyavlenskij, O. I., Exact solutions to the Navier–Stokes equations, Comptes Rendus Math. Acad. Sci. Soc. R. Canada, Vol. 24, No. 4, pp. 138–143, 2002.
Bogoyavlenskij, O. I., Exact solutions to the Navier–Stokes equations equations and viscous MHD equations, Phys. Letters A, Vol. 307, No. 5–6, pp. 281–286, 2003.
Boisvert, R. E., Ames, W. F., and Srivastava, U. N., Group properties and new solutions of Navier–Stokes equations, J. Eng. Math., Vol. 17, pp. 203–221, 1983.
Boldea, C.-R., A generalization for peakon's solitary wave and Camassa–Holm equation, General Math., Vol. 5, No. 1–4, pp. 33–42, 1995.
Boltyanskii, V. G. and Vilenkin, N. Ya., Symmetry in Algebra, 2nd ed. [in Russian], Nauka, Moscow, 2002.
Bona, J. L. and Schonbek, M. E., Travelling-wave solutions to the Korteweg–de Vries–Burgers equation, Proc. Roy. Soc. Edinburgh, Sect. A, Vol. 101, pp. 207–226, 1985.
Born, M. and Infeld, L., Foundations of a new field theory, Proc. Roy. Soc. London, Ser. A, Vol. 144, No. 5, pp. 425–451, 1934.
Boussinesq, J., Sur l'influence des frottements dans les mouvements regulieres des fluides, J. Math. Pure Appl., Vol. 33, pp. 377–438, 1868.
Boussinesq, J., Theorie generale des mouvements qui sont propages dans un canal rectangulaire horizontal, Comptes Rendus Acad. Sci., Paris, Vol. 73, pp. 256–260, 1971.
Boussinesq, J., Theorie des ondes et des remous qui se propagent le long dune canal rectangulaire horizontal, et communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond, J. Math. Pures Appl., Ser. 2, Vol. 17, pp. 55–108, 1872.
Boussinesq, J., Recherches theorique sur lecoulement des nappes deau infiltrees dans le sol et sur le debit des sources, J. Math. Pures Appl., Vol. 10, No. 1, pp. 5–78, 1904.
Bowen, W. R. and Williams, P. M., Finite difference solution of the 2-dimensional Poisson–Boltzmann equation for spheres in confined geometries, Colloids and Surfaces A: Physicochem. and Eng. Aspects, Vol. 204, pp. 103–115, 2002.
Brady, J. F. and Acrivos, A., Steady flow in a channel or tube with an accelerating surface velocity. An exact solution to the Navier–Stokes equations with reverse flow, J. Fluid Mech., Vol. 112, pp. 127–150, 1981.
Brady, J. F. and Durlofsky, L., On rotating disk flow, J. Fluid Mech., Vol. 175, pp. 363–394, 1987.
Bratus', A. S. and Volosov, K. A., Exact solutions of the Hamilton–Jacobi–Bellman equation for problems of optimal correction with an integral constraint on the total control resource [in Russian], Doklady RAN, Vol. 385, No. 3, pp. 319–322, 2002.
Brennen, C. E., Fundamentals of Multiphase Flow, Cambridge Univ. Press, 2005
Bressan, A., Hyperbolic Systems of Conservation Laws: The One-Dimensional Cauchy Problem, Oxford University Press, 2000.
Bressan, A. and Constantin, A., Global solutions of the Hunter–Saxton equation, SIAM J. Math. Anal., Vol. 37, No. 3, 996–1026, 2005.
Bressan, A. and Constantin, A., Global conservative solutions of the Camassa–Holm equation, Arch. Ration. Mech. Anal., Vol. 183, No. 2, pp. 215–239, 2007\,a.
Bressan, A. and Constantin, A., Global dissipative solutions of the Camassa–Holm equation, Anal. Appl., Vol.5, pp. 1–27, 2007\,b.
Bretherton, F. P., The motion of long bubbles in tubes, J. Fluid Mech., Vol. 10, No. 2, pp. 166–168, 1962.
Bridgman, P. W., Dimensional Analysis, Yale Univ. Press, New Haven, 1931.
Broman, G. I. and Rudenko, O. V., Submerged Landau jet: exact solutions, their meaning and application, Physics-Uspekhi, Vol. 53, No. 1, pp. 91–98, 2010.
Bryant, P. J. and Stiassnie M., Different forms for nonlinear standing waves in deep water, J. Fluid Mech., Vol. 272, pp. 135–156, 1994.
Buchnev, A. A., A Lie group admitted by the ideal incompressible fluid equations [in Russian], In: Dinamika Sploshnoi Sredy, No. 7, Inst. gidrodinamiki AN USSR, Novosibirsk, pp. 212–214, 1971.
Buckley, S. E. and Leverett, M. C., Mechanisms of oil displacement in sands, Trans. AIME, Vol. 142, pp. 107–116, 1942.
Bullough, R. K., Solitons, In: Interaction of Radiation and Condensed Matter, Vol. 1, IAEA–SMR–20/51 (International Atomic Energy Agency, Vienna), pp. 381–469, 1977.
Bullough, R. K., Solitons, Phys. Bull., February, pp. 78–82, 1978.
Bullough, R. K. and Caudrey, P. J. (Eds.), Solitons, Springer-Verlag, Berlin, 1980.
Burde, G. I., On the motion of fluid near a stretching circular cylinder, J. Appl. Math. Mech. (PMM), Vol. 53, pp. 271–273, 1989.
Burde, G. I., The construction of special explicit solutions of the boundary-layer equations. Steady flows, Quart. J. Mech. Appl. Math., Vol. 47, No. 2, pp. 247–260, 1994.
Burde, G. I., The construction of special explicit solutions of the boundary-layer equations. Unsteady flows, Quart. J. Mech. Appl. Math., Vol. 48, No. 4, pp. 611–633, 1995.
Burde, G. I., New similarity reductions of the steady-state boundary-layer equations, J. Phys. A: Math. Gen., Vol. 29, No. 8, pp. 1665–1683, 1996.
Burde, G. I., Potential symmetries of the nonlinear wave equation u_tt = (uu_x)_x and related exact and approximate solutions, J. Phys. A., Vol. 34, pp. 5355–5371, 2001.
Burgan, J. R., Munier, A., Feix, M. R., and Fijalkow, E., Homology and the nonlinear heat diffusion equation, SIAM J. Appl. Math., Vol. 44, No. 1, pp. 11–18, 1984.
Burgers, J. M., A mathematical model illustrating the theory of turbulence, Adv. Appl. Mech., Vol. 1, pp. 171–199, 1948.
Burt, P. B., Exact, multiple soliton solutions of the double sine-Gordon equation, Proc. Roy. Soc. London, Ser. A, Vol. 359, pp. 479–495, 1978.
Bytev, V. O., Nonsteady motion of a rotating ring of viscous incompressible fluid with free boundary, J. Appl. Mech. Tech. Phys., No. 3, p. 83, 1970.
Bytev, V. O., Group properties of the Navier–Stokes equations [in Russian], Numerical Methods in Continuum Mechanics (Novosibirsk), Vol. 3, No. 3, pp. 13–17, 1972.
Bytev, V. O., Invariant solutions of the Navier–Stokes equations, J. Appl. Mech. Tech. Phys., No. 6, p. 56, 1972.
Calmet, J. and van Hulzen, J. A., Computer Algebra Systems. Computer Algebra: Symbolic and Algebraic Computations, Springer, New York, 2nd ed., 1983.
Calogero, F., A solvable nonlinear wave equation, Stud. Appl. Math., Vol. 70, No. 3, pp. 189–199, 1984.
Calogero, F., Universality and integrability of the nonlinear evolution PDEs describing N-wave interactions, J. Math. Phys., Vol. 30, No. 1, pp. 28–40, 1989.
Calogero, F. and Degasperis, A., Nonlinear evolution equations solvable by the inverse spectral transform. I, Nuovo Cimento B, Vol. 32, pp. 201–242, 1976.
Calogero, F. and Degasperis, A., Spectral Transform and Solitons: Tolls to Solve and Investigate Nonlinear Evolution Equations, North-Holland Publishing Company, Amsterdam, 1982.
Camassa, R. and Holm, D. D., An integrable shallow water equation with peaked solitons, Phys. Rev. Letter, Vol. 71, No. 11, pp. 1661–1664, 1993.
Camassa, R., Holm, D. D., and Hyman, J. M., A new integrable shallow water equation, Adv. Appl. Mech., Vol. 31, pp. 1–33, 1994.
Camassa, R. and Zenchuk, A. I., On the initial value problem for a completely integrable shallow water equation, Phys. Letters A, Vol. 281, pp. 26–33, 2001.
Cantwell, B. J., Similarity transformations for the two-dimensional, unsteady, stream function equation, J. Fluid Mech., Vol. 85, No. 2, pp. 257–271, 1978.
Cantwell, B. J., Introduction to Symmetry Analysis, Cambridge Univ. Press, Cambridge, 2002.
Cariello, F. and Tabor, M., Painleve expansions for nonintegrable evolution equations, Physica D, Vol. 39, No. 1, pp. 77–94, 1989.
Carnie, S. L., Chan, D. Y. C., and Stankovich, J., Computation of forces between spherical colloidal particles: nonlinear Poisson–Boltzmann theory, J. Colloid Interface Sci., Vol. 165, pp. 116–128, 1994.
Carslaw, H. S. and Jaeger, J. C., Conduction of Heat in Solids, Clarendon Press, Oxford, 1984.
Castillo, E. and Ruiz-Cobo, M. R., Functional Equations and Modelling in Science and Engineering, Marcel Dekker, New York, 1992.
Castillo, E. and Ruiz-Cobo, R., Functional Equations in Applied Sciences, Elsevier, New York, 2005.
Cavalcante, J. A. and Tenenblat, K., Conservation laws for nonlinear evolution equations, J. Math. Physics, Vol. 29, No. 4, pp. 1044–1049, 1988.
Chadan, K., Colton, D., Paivarinta, L., and Rundell, W., An Introduction to Inverse Scattering and Inverse Spectral Problems, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1997.
Chaplygin, S. A., Gas jets, Uchenye Zapiski Imper. Univ., Otdel. Fiz.-Mat., Vol. 21, pp. 1–121, 1904; GITTL, Moscow–Leningrad, 1949; Tech. Memos. Nat. Adv. Comm. Aeronaut., No. 1063, 112 pp., 1944.
Char, B. W., Geddes, K. O., Gonnet, G. H., Monagan, M. B., and Watt, S. M., Maple Reference Manual, Waterloo Maple Publishing, Waterloo, Ontario, Canada, 1990.
Cheb-Terrab, E. S. and von Bulow, K., A computational approach for the analytical solving of partial differential equations, Computer Physics Communications, Vol. 90, pp. 102–116, 1995.
Cheng, E. H. W., Ozisik, M. N., and Williams III, J. C., Nonsteady three-dimensional stagnation-point flow, J. Appl. Mech., Vol. 38, pp. 282–287, 1971.
Cherniha, R. M., Conditional symmetries for systems of PDEs: new definitions and their application for reaction–diffusion systems, J. Phys. A: Math. Theor., Vol. 43 (405207), p. 13, 2010.
Cherniha, R. M. and Davydovych, V., Conditional symmetries and exact solutions of the diffuse Lotka–Volterra system, arXiv: 1012.5747v1 [math-ph], 2010.
Cherniha, R. M. and Dutka, V. A., Diffusive Lotka–Volterra system: Lie symmetries and exact and numerical solutions, Ukrainian Math. J., Vol. 56, No. 10, pp. 1665–1675, 2004.
Cherniha, R. M. and King, J. R., Lie symmetries of nonlinear multidimensional reaction-diffusion systems: I, J. Phys. A: Math. Gen., Vol. 33, pp. 267–282, 7839–7841, 2000.
Cherniha, R. M. and King, J. R., Lie symmetries of nonlinear multidimensional reaction-diffusion systems: II, J. Phys. A: Math. Gen., Vol. 36, pp. 405–425, 2003.
Cherniha, R. M. and Myroniuk, L., New exact solutions of a nonlinear cross-diffusion system J. Phys. A: Math. Theor., Vol. 41 (395204), 2008.
Chernousko, F. L., Self-similar solutions of the Bellman equation for optimal correction of random disturbances, Appl. Math. and Mech. (PMM), Vol. 35, No. 2, pp. 291–300, 1971.
Chernousko, F. L. and Kolmanovskii, V. B., Optimal Control with Random Disturbances [in Russian], Nauka, Moscow, 1978.
Chernyi, G. G., Gas Dynamics [in Russian], Nauka, Moscow, 1988.
Chipot, M. (Ed.), Handbook of Differential Equations. Stationary Partial Differential Equations, Vols 4 and 5, Elsevier, Amsterdam, 2007 and 2008.
Chipot, M. and Quittner, P. (Eds.), Handbook of Differential Equations. Stationary Partial Differential Equations, Vols 1–3, Elsevier, Amsterdam, 2004–2006.
Chou, T., Symmetries and a hierarchy of the general KdV equation, J. Phys. A, Vol. 20, pp. 359–366, 1987.
Chowdhury, A. R., Painleve Analysis and Its Applications, Chapman Hall/CRC Press, Boca Raton, 2000.
Chun, C., Soliton and periodic solutions for the fifth-order KdV equation with the Exp-function method, Physics Letters A, Vol. 372, No. 16, pp. 2760–2766, 2008.
Cicogna, G., ``Weak'' symmetries and adopted variables for differential equations, Int. J. Geometric Meth. Modern Phys., Vol. 1, No. 1–2, pp. 23–31, 2004.
Citti, G., Pascucci, A., and Polidoro S., On the regularity of solutions to a nonlinear ultraparabolic equation arising in mathematical finance, Differential Integral Equations, Vol. 14, No. 6, pp. 701–738, 2001.
Clarkson, P. A., Painleve analysis of the damped, driven nonlinear Schrodinger equation, Proc. Roy. Soc. Edinburgh, Vol. 109A, No. 1, pp. 109–126, 1988.
Clarkson, P. A., Nonclassical symmetry reductions for the Boussinesq equation, Chaos, Solitons and Fractals, Vol. 5, pp. 2261–2301, 1995.
Clarkson, P. A., Fokas, A. S., and Ablowitz, M. J., Hodograph transformations on linearizable partial differential equations, SIAM J. Appl. Math., Vol. 49, pp. 1188–1209, 1989.
Clarkson, P. A. and Hood, S., Nonclassical symmetry reductions and exact solutions of the Zabolotskaya–Khokhlov equation, Eur. J. Appl. Math., Vol. 3, pp. 381–415, 1992.
Clarkson, P. A. and Kruskal, M. D., New similarity reductions of the Boussinesq equation, J. Math. Phys., Vol. 30, No. 10, pp. 2201–2213, 1989.
Clarkson, P. A., Ludlow, D. K., and Priestley, T. J., The classical, direct and nonclassical methods for symmetry reductions of nonlinear partial differential equations, Methods and Applications of Analysis, Vol. 4, No. 2, pp. 173–195, 1997.
Clarkson, P. A. and Mansfield, E. L., Symmetry reductions and exact solutions of a class of nonlinear heat equations, Physica D, Vol. 70, No. 3, pp. 250–288, 1994.
Clarkson, P. A., McLeod, J. B., Olver, P. J., and Ramani, R., Integrability of Klein–Gordon equations, SIAM J. Math. Anal., Vol. 17, pp. 798–802, 1986.
Clarkson, P. A. and Priestley, T. J., On a shallow water wave system, Stud. Appl. Math., Vol. 101, pp. 389–432, 1998.
Clarkson, P. A. and Winternitz, P., Nonclassical symmetry reductions for the Kadomtsev–Petviashvili equation, Physica D, Vol. 49, pp. 257–272, 1991.
Cochran, W. G., The flow due to a rotating disc, Proc. Cambridge Philos. Soc., Vol. 30, pp. 365–375, 1934.
Coclite, G. M. and Karlsen, K. H., On the well-posedness of the Degasperis–Procesi equation, J. Funct. Anal., Vol. 233, No. 1, pp. 60–91, 2006.
Cohen, B. J., Krommes, J. A., Tang, W. M., and Rosenbluth, M. N., Nonlinear saturation of the dissipative trapped-ion mode by mode coupling, Nuclear Fusion, Vol. 16, No. 6, pp. 971–992, 1976.
Cole, J. D., On a quasi-linear parabolic equation occurring in aerodynamics, Quart. Appl. Math., Vol. 9, No. 3, pp. 225–236, 1951.
Cole, J. D. and Cook, L. P., Transonic Aerodynamics, North-Holland, Amsterdam, 1986.
Concus, P., Standing capillary-gravity waves of finite amplitude, J. Fluid Mech., Vol. 14, pp. 568–576, 1962.
Constantin, A. and Escher, J., Wave breaking for nonlinear nonlocal shallow water equations, Acta Math., Vol. 181, No. 2, pp. 229–243, 1998.
Constantin, A., Gerdjikov, V. S., and Ivanov, R. I., Inverse scattering transform for the Camassa–Holm equation, Inverse Problems, Vol. 22, No. 6, pp. 2197–2207, 2006.
Conte, R., Invariant Painleve analysis for partial differential equations, Phys. Lett., Ser. A, Vol. 140, No. 7–8, pp. 383–390, 1989.
Conte, R. (Ed.), The Painleve Property. One Century Later, Springer-Verlag, New York, 1999.
Conte, R., Exact solutions of nonlinear partial differential equations by singularity analysis, Lect. Notes Phys., Vol. 632, pp. 1–83, 2003.
Conte, R. and Musette, M., Painleve analysis and Backlund transformation in the Kuramoto–Sivashinsky equation, J. Phys. A, Vol. 22, pp. 169–177, 1989.
Conte, R. and Musette, M., Linearity inside nonlinearity: Exact solutions to the complex Ginzburg–Landau equation, Physica D, Vol. 69, No. 1, pp. 1–17, 1993.
Conte, R. and Musette, M., The Painleve Handbook, Springer, 2008.
Corless, R. M., Essential Maple, Springer, Berlin, 1995.
Couette, M., Etudes sur le frottement des liquides, Ann. Chim. Phys., Vol. 21, No. 6, pp. 433–510, 1890.
Courant, R., Partial Differential Equations, InterScience, New York, 1962.
Courant, R. and Friedrichs, R., Supersonic Flow and Shock Waves, Springer-Verlag, New York, 1985.
Courant, R. and Hilbert, D., Methods of Mathematical Physics, Vol. 2, Wiley–Interscience Publ., New York, 1989.
Cox, S. M., Nonaxisymmetric flow between an air table and a floating disk, Phys. Fluids, Vol. 14, pp. 1540–1543, 2002.
Crabtree, F. L., Kuchemann, D., and Sowerby, L., In: Laminar Boundary Layers (Ed. L. Rosenhead), Oxford University Press, Oxford, 1963.
Craik, A., The stability of unbounded two- and three-dimensional flows subject to body forces: some exact solutions, J. Fluid Mech., Vol. 198, pp. 275–292, 1989.
Crandall, M. G., Evans, L. C., and Lions, P.-L., Some properties of viscosity solutions of Hamilton–Jacobi equations, Trans. Amer. Math. Soc., Vol. 283, No. 2, pp. 487–502, 1984.
Crandall, M. G., Ishii, H., and Lions, P.-L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., Vol. 27, No. 1, pp. 1–67, 1992.
Crandall, M. G. and Lions, P.-L., Viscosity solutions of Hamilton–Jacobi equations, Trans. Amer. Math. Soc., Vol. 277, No. 1, pp. 1–42, 1983.
Crane, L. J., Flow past a stretching plate, Z. Angew. Math. Phys. (ZAMP), Vol. 21, pp. 645–647, 1970.
Crank, J., The Mathematics of Diffusion, Clarendon Press, Oxford, 1975.
Crank, J. and Nicolson, P., A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, Proc. Camb. Philos. Soc., Vol. 43, pp. 50–67, 1947.
Crudeli, U., Sui moti di un liquido viscoso (omogeno) simmetrici rispetto ad un asse, Atti Reale Accad. Naz. dei Lincei. Rendiconti, Ser. 6, Vol. 5, No. 7, pp. 500–504, 1927.
Crudeli, U., Una nuova categoria di moti stazionary dei liquidi (pesanty) viscosi entro tubi cilindrici (rotondi) verticali, Atti Reale Accad. Naz. dei Lincei. Rendiconti, Ser. 6, Vol. 5, No. 10, pp. 783–789, 1927.
Crudeli, U., Sopra una categoria di moti stazionary dei liquidi (pesanty) viscosi entro tubi cilindrici (rotondi) verticali, Atti Reale Accad. Naz. dei Lincei. Rendiconti, Ser. 6, Vol. 6, No. 10, pp. 397–401, 1927.
Cunning, G. M., Davis, A. M. J., and Weidman, P. D., Radial stagnation flow on a rotating circular cylinder with uniform transpiration, J. Eng. Math., Vol. 33, pp. 113–128, 1998.
Czerwik, S., Functional Equations and Inequalities in Several Variables, World Scientific Publ., Singapore, 2002.
Dafermos, C. M., Hyperbolic Systems of Conservation Laws, In: Systems of Non-Linear Partial Differential Equations, (Eds. D. Reidel and J. S. Ball), Kluwer, Dordrecht, pp. 24-70, 1983.
Dafermos, C. M., Hyperbolic Conservation Laws in Continuum Physics, Springer-Verlag, Berlin, 2000.
Dafermos, C. M. and Feireisl, E. (Eds.), Handbook of Differential Equations. Evolutionary Equations, Vols 1–3, Elsevier, Amsterdam, 2004–2006.
Dafermos, C. M. and Pokorny M. (Eds.), Handbook of Differential Equations. Evolutionary Equations, Vols 4 and 5, Elsevier, Amsterdam, 2008 and 2009.
Danberg, J. E. and Fansler, K. S., A nonsimilar moving-wall boundary-layer problem, Q. Appl. Math., Vol. 33, pp. 305–309, 1976.
Danilov, V. G. and Subochev, P. Yu., Wave solutions of semilinear parabolic equations, Theor. Math. Phys., Vol. 89, No. 1, pp. 1029–1045, 1991.
Danilov, V. G., Maslov V. P., and Volosov, K. A., Mathematical Modelling of Heat and Mass Transfer Processes, Kluwer, Dordrecht, 1995.
Dankwerts, P. V., Gas–Liquid Reactions, McGraw-Hill, New York, 1970.
Daroczy, Z. and Pales, Z. (Eds.), Functional Equations\dash Results and Advances, Kluwer Academic, Dordrecht, 2002.
Dauenhauer, E. C. and Majdalani, J., Exact self-similarity solution of the Navier–Stokes equations for a porous channel with orthogonally moving walls, Phys. Fluids, Vol. 15, pp. 1485–1495, 2003.
Dauxois, T. and Peyrard, M., Physics of Solitons, Cambridge University Press, Cambridge, 2006.
Davenport, J. H., Siret, Y. and Tournier, E., Computer Algebra Systems and Algorithms for Algebraic Computation, Academic Press, London, 1993.
Davey, A., Boundary-layer flow at a saddle point of attachment, J. Fluid Mech., Vol. 10, pp. 593–610, 1961.
Davey, A. and Schofield, D., Three-dimensional flow near a two-dimensional stagnation point, J. Fluid Mech., Vol. 28, pp. 149–151, 1967.
Debler, W. R. and Montgomery, R. D., Flow over an oscillating plate with suction or with an intermediate film: two exact solutions of the Navier–Stokes equations, J. Appl. Math., Vol. 38, pp. 262–265, 1971.
Debnath, L., Nonlinear Partial Differential Equations for Scientists and Engineers, Birkhauser, Boston, MA, 2nd ed., 2005.
Degasperis, A., Holm, D. D., and Hone, A. N. W., A new integrable equation with peakon solutions, Theor. Math. Phys., Vol. 33, No. 2, pp. 1463–1474, 2002.
Degasperis, A. and Procesi, M., Asymptotic integrability, In: Symmetry and Perturbation Theory (Eds. A. Degasperis and G. Gaeta), World Scientific, NJ, pp. 23–37, 1999.
Dehghan, M. and Shokri, A., Numerical solution of the nonlinear Klein–Gordon equation using radial basis functions, J. Comp. Appl. Math., Vol. 230, No. 2, pp. 400–410, 2009.
Devi, C. D. S., Takhar, H. S., and Nath, G., Unsteady, three-dimensional, boundary-layer flow due to a stretching surface, Int. J. Heat Mass Transfer, Vol. 29, pp. 1996–1999, 1986.
Dey, B., Compacton solutions for a class of two parameter generalized odd-order Korteweg–de Vries equations, Phys. Rev. E, Vol. 57, pp. 4733-4738, 1998.
Dickey, L. A., Soliton Equations and Hamilton Systems, World Scientific, Singapore, 1991.
Dobrokhotov, S. Yu. and Tirozzi, B., Localized solutions of one-dimensional non-linear shallow-water equations with velocity c = x^1/2, Rus. Math. Surveys, Vol. 65, No. 1, pp. 177–179, 2010.
Dobryshman, E. M., On some singularities of fields of pressure and wind in equatorial region. Report on the conference on common atmospheric circulation, Moscow, 1964.
Dodd, R. K. and Bullough, R. K., Polynomial conserved densities for the sine-Gordon equations, Proc. Roy. Soc. London, Ser. A, Vol. 352, pp. 481–503, 1977.
Dodd, R. K., Eilbeck, J. C., Gibbon, J. D., and Morris, H. C., Solitons and Nonlinear Wave Equations, Academic Press, London, 1982.
Dolidze, D. E., On some cases of rotation of a viscous incompressible fluid, Izvestiya AN SSSR. Otdelenie tekhn. nauk [in Russian], No. 2, pp. 197–208, 1937.
Dommelen, L. L. van and Shen, S. F., The spontaneous generation of the singularity in a separating laminar boundary layer, J. Comput. Phys., Vol. 38, pp. 125–140, 1980.
Dorfman, I. Ya., The Krichever–Novikov equation and local symplectic structures, Sov. Math. Dokl., Vol. 38, pp. 340–343, 1989.
Dorfman, I. Ya., Dirac Structures and Integrability of Nonlinear Evolution Equations, Wiley, Chichester, 1993.
Dorodnitsyn, V. A., Group Properties and Invariant Solutions of Nonlinear Heat Equations with a Source or Sink [in Russian], Preprint No. 74, Keldysh Institute of Applied Mathematics, Academy of Sciences, USSR, Moscow, 1979.
Dorodnitsyn, V. A., On invariant solutions of the nonlinear heat equation with a source [in Russian], Zhurn. vychisl. matem. i matem. fiziki, Vol. 22, No. 6, pp. 1393–1400, 1982.
Dorodnitsyn, V. A. and Elenin, G. G. Symmetry in Solutions of Equations of Mathematical Physics [in Russian], Znanie (No. 4), Moscow, 1984.
Dorodnitsyn, V. A., Knyazeva, I. V., and Svirshchevskii, S. R., Group properties of the heat equation with a source in two and three dimensions [in Russian], Diff. Uravneniya, Vol. 19, No. 7, pp. 1215–1223, 1983.
Dorodnitsyn, V. A. and Svirshchevskii, S. R., On Lie–Backlund Groups Admitted by the Heat Equation with a Source [in Russian], Preprint No. 101, Keldysh Institute of Applied Mathematics, Academy of Sciences, USSR, Moscow, 1983.
Dorrepaal, J. M., An exact solution of the Navier–Stokes equation which describes non-orthogonal stagnation point flow in two dimensions, J. Fluid Mech., Vol. 163, pp. 141–147, 1986.
Doyle, Ph. W., Separation of variables for scalar evolution equations in one space dimension, J. Phys. A: Math. Gen., Vol. 29, pp. 7581–7595, 1996.
Doyle, Ph. W. and Vassiliou, P. J., Separation of variables for the 1-dimensional non-linear diffusion equation, Int. J. Non-Linear Mech., Vol. 33, No. 2, pp. 315–326, 1998.
Drazin, P. G. and Johnson, R. S., Solitons: An Introduction, Cambridge Univ. Press, Cambridge, 1989 and 1996.
Drazin, P. G. and Riley, N., The Navier–Stokes Equations: A Classification of Flows and Exact Solutions, Cambridge Univ. Press, Cambridge, 2006.
Dresner, L., Similarity Solutions of Nonlinear Partial Differential Equations, Pitman, Boston, 1983.
Dryuma, V. S., On an analytic solution of the two-dimensional Korteweg–de Vries equation [in Russian], Pis'ma v ZhETF, Vol. 19, No. 7, pp. 753–757, 1974.
Dryuma, V. S., On initial values problem in theory of the second order ODE's, pp. 109–116, In: Proc. Workshop on Nonlinearity, Integrability, and All That: Twenty Years after NEEDS'79, (Eds. M. Boiti, L. Martina, F. Pempinelli, B. Prinari, and G. Soliani), World Scientific, Singapore, 2000.
Dryuma, V. S., On solutions of Heavenly equations and their generalizations, arXiv:gr-qc–0611001v1, 2006.
Dryuma, V. S., On spaces related to the Navier–Stokes equations, Buletinul Academiei de Stiinte a Republicii Moldova. Matematica, Vol. 64, No. 3, pp. 107–110, 2010.
Dubinskii, Yu. A., Analytic Pseudo-Differential Operators and Their Applications, Kluwer, Dordrecht, 1991.
Dubrovin, B. A., Geometry of 2D Topological Field Theories, Lect. Notes in Math., Vol. 1620, pp. 120–348, Springer-Verlag, Berlin, 1996.
Dubrovin, B. A. and Novikov, S. P., Hamiltonian formalism of hydrodynamic-type systems. The averaging method for field-theoretic systems, Doklady AN SSSR, Vol. 270, No. 4, pp. 781–785, 1983.
Dubrovin, B. A. and Novikov, S. P., Hydrodynamics of weakly deformed soliton grids. Differential geometry and Hamiltonian theory, Uspekhi mat. nauk, Vol. 44, No. 6, pp. 29–98, 1989.
Duffy, B. R. and Parkes, E. J., Travelling solitary wave solutions to a seventh-order generalized KdV equation, Phys. Lett. A, Vol. 214, 271–272, 1996.
Edwards, M. P., Classical symmetry reductions of nonlinear diffusion-convection equations, Phys. Letters A, Vol. 190, pp. 149–154, 1994.
Eglit, E. E. and Hodges, D. H. (Eds.), Continuum Mechanics via Problems and Exercises, Vol. 1, World Scientific, Singapore, 1996.
Ekman, V. W., On the influence of the Earth's rotation on ocean currents, Arkiv. Mat. Astron. Fys., Vol. 2, pp. 1–52, 1905.
Emech, Y. P. and Taranov, V. B., Group properties and invariant solutions of electric field equations at nonlinear Ohm law [in Russian], Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 28–36, 1972.
Enneper, A., Uber asymptotische Linien, Nachr. Konigl. Gesellsch. d. Wissenschaften Gottingen, p. 493–511, 1870.
Erbas, B. and Yusufoglu, E., Exp-function method for constructing exact solutions of Sharma–Tasso–Olver equation. Chaos, Solitons and Fractals, Vol. 41, No. 5, pp. 2326–2330, 2009.
Ershov, L. V., Ivlev, D. D., and Romanov, A. V., On generalization of Prandtl solution for compression of plastic layer, In: Modern Problems of Aviation and Mechanics [in Russian], Moscow, p. 137, 1982.
Escher, J., Liu, Y., and Yin, Z., Global weak solutions and blow-up structure for the Degasperis–Procesi equation, J. Funct. Anal., Vol. 241, No. 2, pp. 457–485, 2006.
Escher, J., Liu, Y., and Yin, Z., Shock waves and blow-up phenomena for the periodic Degasperis–Procesi equation, Indiana Univ. Math. J., Vol. 56, No. 1, pp. 87–117, 2007.
Estevez, P. G., Non-classical symmetry and the singular manifold: the Burgers and the Burgers–Huxley equation, J. Phys. A: Math. Gen., Vol. 27, pp. 2113–2127, 1994.
Estevez, P. G. and Gordoa, P. R., Painleve analysis of the generalized Burgers–Huxley equation, J. Phys. A: Math. Gen., Vol. 23, p. 4831, 1990.
Estevez, P. G., Qu, C. Z., and Zhang, S. L., Separation of variables of a generalized porous medium equation with nonlinear source, J. Math. Anal. Appl., Vol. 275, pp. 44–59, 2002.
Euler, N., Gandarias, M. L., Euler, M., and Lindblom, O., Auto-hodograph transformations for a hierarchy of nonlinear evolution equations, J. Math. Anal. Appl., Vol. 257, No. 1, pp. 21–28, 2001.
Faber, T. E., Fluid Dynamics for Physicists, Cambridge Univ. Press, Cambridge, 1995.
Faddeev, L. D. (Ed.), Mathematical Physics: Encyclopedia [in Russian], Bol'shaya Rossiiskaya Entsiklopediya, Moscow, 1998.
Faddeev, L. D. and Takhtajan, L. A., Hamiltonian Methods in the Theory of Solitons, Springer-Verlag, Berlin, 1987.
Falkner, V. M. and Skan, S. W., Some approximate solutions of the boundary layer equations, Phil. Mag., Vol. 12, pp. 865–896, 1931.
Fal'kovich, A. I., Group invariant solutions of atmospheric circulation model for the equatorial region, Izvestiya Akad. Nauk USSR, Fizika atmosfery i okeana, Vol. 4, p. 579, 1968.
Farlow, S. J., Partial Differential Equations for Scientists and Engineers, John Wiley Sons, New York, 1982.
Feng, Z., Exact solutions to the Burgers–Korteweg–de Vries equation, J. Phys. Soc. Japan, Vol. 71, pp. 1–4, 2002.
Feng, Z., On traveling wave solutions to modified Burgers–Korteweg–de Vries equation, Phys. Lett. A, Vol. 318, pp. 522–525, 2003.
Feng, Z., An exact solution to the Korteweg–de Vries–Burgers equation, Appl. Math. Lett., Vol. 18, 733–737, 2005.
Feng, Z., On travelling wave solutions of the Burgers–Korteweg–de Vries equation, Nonlinearity, Vol. 20, 343–356, 2007.
Ferapontov, E. V. and Pavlov, M. V., Hydrodynamic reductions of the heavenly equation, arXiv:nlin/0301048v1 [nlin.SI], 2003.
Ferapontov, E. V. and Tsarev, S. P., Equations of hydrodynamic type, arising in gas chromatography. Riemann invariants and exact solutions, Mat. Model., Vol. 3, No. 2, pp. 82–91, 1991.
Filenberger, G., Solitons. Mathematical Method for Physicists, Springer-Verlag, Berlin, 1981.
Filippov, Yu. G., Application of the group invariant method for the solution of the problem on determining nonhomogeneous ocean flows, Meteorologia i Hidrologia, Vol. 9, p. 53, 1968.
Fisher, R. A., The wave of advance of advantageous genes, Annals of Eugenics, 1937, Vol. 7, pp. 355–369.
Fleming, W. H. and Soner, H. M., Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, New York, 1993.
Fokas, A. S. and Anderson, R. L., Group theoretical nature of Backlund transformations, Lett. Math. Phys., Vol. 3, p. 117, 1979.
Fokas, A. S. and Fuchssteiner, B., Backlund transformations for hereditary symmetries, Nonlinear Anal., Vol. 5, pp. 423–432, 1981.
Fokas, A. S. and Yortsos, Y. C., On the exactly solvable equation s_t =[(βs+γ)^-2s_x]_x +α(βs+γ)^-2s_x occurring in two-phase flow in porous media, SIAM J. Appl. Math., Vol. 42, pp. 318–332, 1982.
Forsyth, A. R., Theory of Differential Equations, Part IV, Vol. VI, Partial Differential Equations, Cambridge Univ. Press, Cambridge, 1906. Reprinted: New York, Dover Publ., 1959.
Foursov, M. F. and Vorob'ev, E. M., Solutions of the nonlinear wave equation u_tt = (uu_x)_x invariant under conditional symmetries, J. Phys. A, Vol. 29, pp. 6363–6373, 1996.
Frank-Kamenetskii, D. A., Diffusion and Heat Transfer in Chemical Kinetics [in Russian], Nauka, Moscow, 1987.
Fu, Z., Liu, S., and Liu, Sh., New kinds of solutions to Gardner equation, Chaos, Solitons, and Fractals, Vol. 20, pp. 301–309, 2004.
Fuchssteiner, B., Some tricks from symmetry-toolbox for nonlinear equation: generalizations of the Camassa–Holm equation, Phys. D, Vol. 95, pp. 229–243, 1996.
Fujita, H., The exact pattern of a concentration-dependent diffusion in a semi-infinite medium, Part II, Textile Res., Vol. 22, p. 823, 1952.
Fushchich, W. I., A new method of investigating the group properties of the equations of mathematical physics, Soviet Phys. Dokl., Vol. 24, No. 6, pp. 437–439, 1979.
Fushchich, W. I. and Cherniha, R. M., The Galilean relativistic principle and nonlinear partial differential equations, J. Phys. A., Vol. 18, pp. 3491–3503, 1985.
Fushchich, W. I., Serov, N. I., and Ahmerov, T. K., On the conditional symmetry of the generalized KdV equation, Rep. Ukr. Acad. Sci., A 12, 1991.
Fushchich, W. I., Shtelen, W. M., and Serov, N. I., Symmetry Analysis and Exact Solutions of the Equations of Mathematical Physics, Kluwer, Dordrecht, 1993.
Fushchich, W. I., Shtelen, W. M., and Slavutsky, S. L., Reduction and exact solutions of the Navier–Stokes equations, J. Phys. A: Math. Gen., Vol. 24, pp. 971–984, 1991.
Gaeta, G., Nonlinear Symmetries and Nonlinear Equations, Kluwer, Dordrecht, 1994.
Gagnon, L. and Winternitz P., Lie symmetries of a generalized nonlinear Schrodinger equation. I. The symmetry group and its subgroups, J. Phys. A, Vol. 24, p. 1493, 1988.
Gagnon, L. and Winternitz P., Lie symmetries of a generalized nonlinear Schrodinger equation. II. Exact solutions, J. Phys. A, Vol. 22, p. 469, 1989.
Gagnon, L. and Winternitz, P., Symmetry classes of variable coefficient nonlinear Schrodinger equations, J. Phys. A, Vol. 26, pp. 7061–7076, 1993.
Galaktionov, V. A., On new exact blow-up solutions for nonlinear heat conduction equations with source and applications, Differential and Integral Equations, Vol. 3, No. 5, pp. 863–874, 1990.
Galaktionov, V. A., Quasilinear heat equations with first-order sign-invariants and new explicit solutions, Nonlinear Analys., Theory, Meth. and Applications, Vol. 23, pp. 1595–1621, 1994.
Galaktionov, V. A., Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities, Proc. Roy. Soc. Edinburgh, Sect. A, Vol. 125, No. 2, pp. 225–246, 1995.
Galaktionov, V. A., Ordered invariant sets for nonlinear evolution equations of KdV-type, Comput. Math. Math. Phys., Vol. 39, No. 9, pp. 1499–1505, 1999.
Galaktionov, V. A., Dorodnitsyn, V. A., Elenin, G. G., Kurdyumov, S. P., and Samarskii, A. A., Quasilinear heat conduction equation with source: blow-up, localization, symmetry, exact solutions, asymptotics, structures, In: Modern Mathematical Problems. New Achievements [in Russian], Vol. 28, pp. 95–206, Moscow, VINITI AN USSR, 1986 (English translation: Plenum Press, New York, 1987).
Galaktionov, V. A. and Posashkov, S. A., On new exact solutions of parabolic equations with quadratic nonlinearities, Zh. Vych. Matem. i Mat. Fiziki [in Russian], Vol. 29, No. 4, pp. 497–506, 1989.
Galaktionov, V. A. and Posashkov, S. A., Exact solutions and invariant subspace for nonlinear gradient-diffusion equations, Zh. Vych. Matem. i Mat. Fiziki [in Russian], Vol. 34, No. 3, pp. 374–383, 1994.
Galaktionov, V. A., Posashkov, S. A., and Svirshchevskii, S. R., On invariant sets and explicit solutions of nonlinear evolution equations with quadratic nonlinearities, Differential and Integral Equations, Vol. 8, No. 8, pp. 1997–2024, 1995.
Galaktionov, V. A., Posashkov, S. A., and Svirshchevskii, S. R., Generalized separation of variables for differential equations with polynomial right-hand sides, Dif. Uravneniya [in Russian], Vol. 31, No. 2, pp. 253–261, 1995.
Galaktionov, V. A. and Svirshchevskii, S. R., Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics, Chapman Hall/CRC Press, Boca Raton, 2006.
Galaktionov, V. A. and Vazques, J. L., Blow-up for a class of solutions with free boundaries for the Navier–Stokes equations, Adv. Diff. Eq., Vol. 4, pp. 297–321, 1999.
Ganji, Z. Z., Ganji, D. D., and Bararnia, H., Approximate general and explicit solutions of nonlinear BBMB equations by Exp-function method, Applied Mathematical Modeling, Vol. 33, No. 4, pp. 1836–1841, 2009.
Ganzha, E. I., An analogue of the Moutard transformation for the Goursat equation θ_xy= 2(λθ_xθ_y)^1/2, Theor. Math. Phys., Vol. 122, No. 1, pp. 35–45, 2000.
Gardner, C. S., Greene, J. M., Kruskal, M. D., and Miura, R. M., Method for solving the Korteweg–de Vries equation, Phys. Rev. Lett., Vol. 19, No. 19, pp. 1095–1097, 1967.
Gardner, C. S., Greene, J. M., Kruskal, M. D., and Miura, R. M., Korteweg–de Vries equation and generalizations. VI: Methods for exact solution, Comm. Pure Appl. Math., Vol. 27, pp. 97–133, 1974.
Geddes, K. O., Czapor, S. R., and Labahn, G., Algorithms for Computer Algebra, Kluwer Academic Publishers, Boston, MA, 1992.
Gelfand, I. M., Some problems of the theory of quasi-linear equations, Uspekhi Matem. Nauk, Vol. 14, No. 2, pp. 87–158, 1959 [Amer. Math. Soc. Translation, Series 2, pp. 295–381, 1963].
Gelfand, I. M. and Levitan B. M., On the determination of a differential equation from its spectral function, Izv. Akad. Nauk USSR, Ser. Math., Vol. 15, No. 4, pp. 309–360, 1951 [Amer. Math. Soc. Translations, Vol. 1, pp. 253–304, 1956].
Geng, X. and Cao, C., Explicit solutions of the 2+1-dimensional breaking soliton equation, Chaos, Solitons and Fractals, Vol. 22, pp. 683–691, 2004.
Gennes, P. G., Wetting: statics and dynamics, Rev. Mod. Phys., Vol. 57, pp. 827–863, 1985.
Gennes, P. G. and Prost, J., The Physics of Liquid Crystals, 2nd ed., Oxford University Press, 1994.
Gesztesy, F. and Weikard, R., Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies–an analytic approach, Bull. AMS, Vol. 35, No. 4, pp. 271–317, 1998.
Getz, C. and Helmstedt, J., Graphics with Mathematica: Fractals, Julia Sets, Patterns and Natural Forms, Elsevier Science Technology Book, Amsterdam, Boston, 2004.
Gibbon, J. D., Fokas, A. S., and Doering, C. R., Dynamically stretched vortices as solutions of the 3D Navier–Stokes equations, Physica D, Vol. 132, pp. 497–510, 1999.
Gibbons, J. and Tsarev, S. P., Conformal maps and reduction of the Benney equations, Phys. Letters A, Vol. 258, No. 4–6, pp. 263–271, 1999.
Gilbarg, G. and Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 2001.
Glassey, R. T., Hunter, J. K., and Zheng, Y., Singularities and oscillations in a nonlinear variational wave equation, In: Singularities and Oscillations (Eds. J. Ranch and M. Taylor), Springer-Verlag, New York, 1997.
Godlewski, E. and Raviart, P.-A., Numerical Approximations of Hyperbolic Systems of Conservation Laws, Springer-Verlag, New York, 1996.
Godreche, C. and Manneville, P. (Eds.), Hydrodynamics and Nonlinear Instabilities, Cambridge Univ. Press, 1998.
Goldshtik, M. A., A paradoxial solution of the Navier–Stokes equations [in Russian], Prik. Mat. Mekh., Vol. 24, pp. 610–621, 1960.
Goldshtik, M. A., Viscous flow paradoxes, Annual Rev. of Fluid Mech., Vol. 22, pp. 441–472, 1990.
Goldshtik, M. A. and Shtern, V. N., Hydrodynamic Stability and Turbulence [in Russian], Nauka, Novosibirsk, 1977.
Goldshtik, M. A. and Shtern, V. N., Loss of symmetry in viscous flow from a linear source, Fluid Dyn., Vol. 24, pp. 151–199, 1989.
Goldshtik, M. A. and Shtern, V. N., Collapse in conical viscous flows, J. Fluid Mech., Vol. 218, pp. 483–508, 1990.
Golovko, V., Kersten, P., Krasil'shchik, I., and Verbovetsky, A., On integrability of the Camassa–Holm equation and its invariants: a geometrical approach, Acta Appl. Math., Vol. 101, No. 1–3, pp. 59–83, 2008.
Golubev, V. V., Lectures on Analytic Theory of Differential Equations [in Russian], GITTL, Moscow, 1950.
Gomes, C. A., Special forms of the fifth-order KdV equation with new periodic and soliton solutions, Appl. Math. Comput., Vol. 189, No. 2, pp. 1066–1077, 2007.
Gorodtsov, V. A., Heat transfer and turbulent diffusion in one-dimensional hydrodynamics without pressure, Appl. Math. and Mech. (PMM), Vol. 62, No. 6, pp. 1021–1028, 1998.
Gorodtsov, V. A., The effect of a local increase in impurity concentration in one-dimensional hydrodynamics, Appl. Math. and Mech. (PMM), Vol. 64, No. 4, pp. 593–600, 2000.
Gortler, H., Verdrangungswirkung der laminaren Grenzschichten und Druck widerstand, Ing. Arch., Vol. 14, pp. 286–305, 1944.
Goursat, M. E., Lecons sur l'integration des equations aux derivees partielles du second order a deux variables independantes, T. 1 , Librairie scientifique A. Hermann, Paris, 1896.
Goursat, M. E., Lecons sur l'integration des equations aux derivees partielles du second order a deux variables independantes, T. 2 , Librairie scientifique A. Hermann, Paris, 1898.
Goursat, E., A Course of Mathematical Analysis. Vol 3. Part 1 [Russian translation], Gostekhizdat, Moscow, 1933.
Grad, H. and Rubin, H., Hydromagnetic equilibria and force-free fields, Proceedings of the 2nd UN Conf. on the Peaceful Uses of Atomic Energy, Geneva, Vol. 31, p. 190, 1958.
Graetz, L., Z. Math. Physik, Bd. 25, S. 316, 375, 1880.
Grauel, A., Sinh-Gordon equation, Painleve property and Backlund transformation, Physica A, Vol. 132, pp. 557–568, 1985.
Grauel, A. and Steeb, W.-H., Similarity solutions of the Euler equations and the Navier–Stokes equations in two space dimensions, Int. J. Theor. Phys., Vol. 24, pp. 255–265, 1985.
Gray, J. W., Mastering Mathematica: Programming Methods and Applications, Academic Press, San Diego, 1994.
Gray, T. and Glynn, J., Exploring Mathematics with Mathematica: Dialogs Concerning Computers and Mathematics, Addison-Wesley, Reading, MA, 1991.
Grebenev, V. N. and Oberlack, M., A geometric interpretation of the second-order structure function arising in turbulence, Math. Phys. Anal. Geom., Vol. 12, pp. 1–18, 2009.
Green, E., Evans, B., and Johnson, J., Exploring Calculus with Mathematica, Wiley, New York, 1994.
Greenhill, A. G., London Math. Soc. Proc., Vol. 13, p. 43, 1881.
Greenspan, H. P., On the motion of a small viscous droplet that wets a surface, J. Fluid Mech., Vol. 84, pp. 125–143, 1978.
Griffiths, G. W. and Schiesser, W. E., Traveling Wave Analysis of Partial Differential Equations: Numerical and Analytical Methods with Matlab and Maple, Academic Press, 2011.
Gromak, V. I., Painleve Differential Equations in the Complex Plane, Walter de Gruyter, Berlin, 2002.
Gromak, V. I. and Lukashevich, N. A., Analytical Properties of Solutions of Painleve Equations [in Russian], Universitetskoe, Minsk, 1990.
Gromak, V. I. and Zinchenko A. S., To the theory of higher-order Paileve equations, Diff. uravneniya, Vol. 40, No. 5, pp. 582–589, 2004.
Grosch, C. E. and Salwen, H., Oscillating stagnation point flow, Proc. Roy. Soc. London, Ser. A, Vol. 384, pp. 175–190, 1982.
Grosheva, M. V. and Efimov, G. B., On Systems of Symbolic Computations [in Russian], In: Applied Program Packages. Analytic Transformations, pp. 30–38. Nauka, Moscow, 1988.
Grundland, A. M. and Infeld, E., A family of non-linear Klein-Gordon equations and their solutions, J. Math. Phys., Vol. 33, pp. 2498–2503, 1992.
Guderley, K. G., The Theory of Transonic Flow, Pergamon, Oxford, 1962.
Guil, F. and Ma nas, M., Loop algebras and the Krichever–Novikov equation, Phys. Lett. A, Vol. 153, pp. 90–94, 1991.
Gupalo, Yu. P., Polyanin, A. D., and Ryazantsev, Yu. S., Mass and Heat Transfer of Reacting Particles with the Flow [in Russian], Nauka, Moscow, 1985.
Gutierres, C. E., The Monge–Ampere Equation, Birkhauser, Boston, 2001.
Gutman, L. N., On structure of breezes, Dokl. TIP, Vol. 1, No. 3, 1947.
Haantjes, A., On X _n-1-forming sets of eigenvectors, Indagationes Mathematicae, Vol. 17, No. 2, pp. 158–162, 1955.
Hagen, G., Uber die Bewegung des Wasser in engen zylindrischen Rohren, Pogg. Ann., Vol. 46, pp. 423–442, 1839.
Hall, P., Balakurmar, P. and Papageorgiu, D., On a class of unsteady three-dimensional Navier–Stokes solutions relevant to rotating disk flows: threshold amplitudes and finite-time singularities, J. Fluid Mech., Vol. 238, pp. 297–323, 1992.
Hamdi, S., Enright, W. H., Schiesser, W. E., and Gottlieb, J. J., Exact solutions of the generalized equal width wave equation, Math. Comp. in Simulation, 2003.
Hamel, G., Spiralformige Bewegungen zaher Flssigkeiten, Jahresbericht der Deutschen Math.-Ver., Vol. 25, pp. 34–60, 1916. Translated as NACA Tech. Memo., No. 1342 (1953).
Hamza, E. A. and MacDonald, D. A., A similar flow between two rotating disks, Quart. Appl. Math., Vol. 41, pp. 495–511, 1984.
Hannah, D. M., Forced flow against a rotating disc, Rep. Mem. Aero. Res. Council, London No. 2772, 1947.
Hanyga, A., Mathematical Theory of Nonlinear Elasticity, PWN, Warszawa, 1985.
Happel, J. and Brenner, H., Low Reynolds Number Hydrodynamics, Prentice-Hall, Englewood Cliffs, 1965.
Harries, D., Solving the Poisson–Boltzmann equation for two parallel cylinders, Langmuir, Vol. 14, pp. 3149–3152, 1998.
Harris, S. E., Conservation laws for a nonlinear wave equation, Nonlinearity, Vol. 9, pp. 187–208, 1996.
Hartree, D. R., On an equation occurring in Falkner and Skan's approximate treatment of the equations of the boundary layer, Proc. Cambr. Phil. Soc., Vol. 33, pp. 223–239, 1937.
Hasimoto, H., Note on Rayleigh's problem for a circular cylinder with uniform suction and related unsteady flow problem, J. Phys. Soc. Jpn., Vol. 11, pp. 611–612, 1956.
Hasimoto, H., Boundary layer growth on a flat plate with suction or injection, J. Phys. Soc. Jpn., Vol. 12, pp. 68–72, 1957.
Hatton, L., Stagnation point flow in a vortex core, Tellus, Vol. 27, pp. 269–280, 1975.
He, J. H. and Abdou, M. A., New periodic solutions for nonlinear evolution equation using Exp-method, Chaos, Solitons and Fractals, Vol. 34, pp. 1421–1429, 2007.
He, J. H. and Wu, X. H., Exp-function method for nonlinear wave equations, Chaos, Solitons and Fractals, Vol. 30, No. 3, pp. 700–708, 2006.
Heck, A., Introduction to Maple, Springer, New York, 3rd ed., 2003.
Heredero, R. H., Shabat, A. B., and Sokolov, V. V., A new class of linearizable equations, J. Phys. A: Math. Gen., Vol. 36, pp. L605–L614, 2003.
Hereman, W., Review of symbolic software for the computation of Lie symmetries of differential equations, Euromath Bull., Vol. 1, pp. 45–82, 1994.
Hereman, W. and Nuseir, A., Symbolic software to construct exact solutions of nonlinear partial differential equations, Math. Comp. Simulation, Vol. 43, pp. 361–378, 1980.
Hereman, W. and Zhaung, W., Symbolic software for solution theory, Acta Appl. Math. Phys. Lett. A, Vol. 76, pp. 13–27, 1997.
Hewitt, R. E., Duck, P. W., and Foster, M. R., Steady boundary-layer solutions for a swirling stratified fluid in a rotating cone, J. Fluid Mech., Vol. 384, pp. 339–374, 1999.
Hewitt, R. E., Duck, P. W., and Stow, S. R., Continua of states in boundary-layer flows, J. Fluid Mech., Vol. 468, pp. 121–152, 2002.
Hiemenz, K., Die Grenzschicht an einem in den gleichformigen Flussigkeitsstrom eingetauchten geraden Kreiszylinder, Dinglers Polytech. J., Vol. 326, pp. 321–324, 344–348, 357–362, 372–374, 407–410, 1911.
Hietarinta, J., A search for bilinear equations passing Hirota's three-soliton condition. I. KdV-type bilinear equations, J. Math. Phys., Vol. 28, No. 8, pp. 1732–1742, 1987.
Hietarinta, J., A search for bilinear equations passing Hirota's three-soliton condition. II. mKdV-type bilinear equations, J. Math. Phys., Vol. 28, No. 9, pp. 2094–2101, 1987.
Hietarinta, J., A search for bilinear equations passing Hirota's three-soliton condition. III. Sine–Gordon-type bilinear equations, J. Math. Phys., Vol. 28, No. 11, pp. 2586–2592, 1987.
Higham, N. J., Functions of Matrices. Theory and Computation, SIAM, Philadelphia, 2008.
Hill, J. M., Solution of Differential Equations by Means of One-Parameter Groups, Pitman, Marshfield, Mass., 1982.
Hill, J. M., Differential Equations and Groups Methods for Scientists and Engineers, CRC Press, Boca Raton, 1992.
Hill, M. J. M., On a spherical vortex, Philos. Trans. Roy. Soc. London, Ser. A, Vol. 185, pp. 213–245, 1894.
Hill, R., A variational principle of maximal plastic work in classical plasticity, Quart. J. Mech. Appl. Math., Vol. 1, pp. 18–28, 1948.
Hinch, E. J. and Lemaitre, J., The effect of viscosity on the height of disks floating above an air table, J. Fluid Mech., Vol. 273, pp. 313–322, 1994.
Hirota, R., Exact solution of the Korteweg–de Vries equation for multiple collisions of solutions, Phys. Rev. Lett., Vol. 27, p. 1192, 1971.
Hirota, R., Exact solution of the Korteweg–de Vries equation for multiple collisions of solutions, J. Phys. Soc. Japan, Vol. 33, No. 3, p. 1455, 1972.
Hirota, R., Exact envelope-soliton solutions of a nonlinear wave equation, J. Math. Phys., Vol. 14, pp. 805–809, 1973.
Hirota, R., Exact N-soliton solution of the wave equation of long waves in shallow water and in nonlinear lattice, J. Math. Phys., Vol. 14, pp. 810–814, 1973.
Hirota, R., Direct methods in soliton theory, pp. 157–176, In: Solitons (Eds. R. K. Bullough and P. J. Caudrey), Springer-Verlag, Berlin, 1980.
Hirota, R., Soliton solutions of a coupled Korteweg–de Vries equation, Phys. Letters A, Vol. 85, No. 8/9, pp. 407–408, 1981.
Hirota, R., The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, 2004.
Hirota, R. and Satsuma, J., Nonlinear evolution equations generated from the Backlund transformation for the Boussinesq equation, Progr. Theor. Phys., Vol. 57, pp. 797–807, 1977.
Hocking, L. M., An example of boundary layer formation, AIAA J., Vol. 1, pp. 1222–1223, 1963.
Hoenselaers, C., Solutions of the hyperbolic sine–Gordon equations, Int. J. Theor. Phys., Vol. 46, 1096–1099, 2007.
Hoffman, A. L., A single fluid model for shock formation in MHD shock tubes, J. Plasma Phys., Vol. 1, pp. 193–207, 1967.
Holodniok, M., Kubicek M., and Hlavacek V., Computation of the flow between two rotating coaxial disk: multiplicity of steady-state solutions, J. Fluid Mech., Vol. 108, pp. 227–240, 1981.
Homann, F., Der Einfluss grosser Zahigkeit bei der Stromung um den Zylinder und um die Kugel, Z. Angew. Math. Mech. (ZAMM), Vol. 16, pp. 153–164, 1936.
Hopf, E., Generalized solutions of nonlinear equations of first order, J. Math. Mech., Vol. 14, pp. 951–973, 1965.
Hopf, E., The partial differential equation u_t + uu_xx = au_xx, Comm. Pure and Appl. Math., Vol. 3, pp. 201–230, 1950.
Howarth, L., On calculation of the steady flow in the boundary layer near the surface of a cylinder in a stream, Rep. ARC, p. 1632, 1934.
Howarth, L., The boundary layer in three-dimensional flow. Part II: The flow near a stagnation point, Philos. Mag., Vol. 42, No. 7, pp. 127–140, 1951.
Hui, W. H., Exact solutions of the unsteady two-dimensional Navier–Stokes equations, Z. Angew. Math. Phys., Vol. 38, pp. 689–702, 1987.
Hunter, J. K. and Saxton, R., Dynamics of director fields, SIAM J. Appl. Math., Vol. 51, No. 6, pp. 1498–1521, 1991.
Hunter, J. K. and Zheng, Y., On a completely integrable nonlinear hyperbolic variational equation, Physica D, Vol. 79, No. 2–4, pp. 361–386, 1994.
Hunter, J. K. and Zheng, Y., On a nonlinear hyperbolic variational equation. I. Global existence of weak solutions, Arch. Rational Mech. Anal., Vol. 129, No. 4, pp. 305–353, 1995.
Hunter, J. K. and Zheng, Y., On a nonlinear hyperbolic variational equation. II. The zero-viscosity and dispersion limits, Arch. Rational Mech. Anal., Vol. 129, No. 4, pp. 355–383, 1995.
Hydon, P. E., Symmetry Methods for Differential Equations: A Beginner's Guide, Cambridge Univ. Press, Cambridge, 2000.
Ibragimov, N. H., Classification of invariant solutions of equations of two-dimensional gas motion. Zh. Prikl. Mekh. Tekh. Fiz., Vol. 4, p. 19, 1966.
Ibragimov, N. H., Group Properties of Some Differential Equations [in Russian], Nauka (Siberian Branch), Novosibirsk, 1967.
Ibragimov, N. H., Transformation Groups Applied in Mathematical Physics, D. Reidel Publ., Dordrecht, 1985.
Ibragimov, N. H., Elementary Lie Group Analysis and Ordinary Differential Equations, John Wiley, Chichester, 1999.
Ibragimov, N. H. (Ed.), CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 1, Symmetries, Exact Solutions and Conservation Laws, CRC Press, Boca Raton, 1994.
Ibragimov, N. H. (Ed.), CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 2, Applications in Engineering and Physical Sciences, CRC Press, Boca Raton, 1995.
Ignatovich, N. V., Invariant-irreducible, partially invariant solutions of steady-state boundary layer equations [in Russian], Mat. Zametki, Vol. 53, No. 1, pp. 140–143, 1993.
Il'ushin, A. A., Continuous Mechanics [in Russian], Moscow Univ., Moscow, 1978.
Infeld, E. and Rowlands, G., Nonlinear Waves, Solitons and Chaos, Cambridge University Press, Cambridge, 2000.
Irmay, S. and Zuzovsky, M., Exact solutions of the Navier–Stokes equations in two-way flows, Isr. J. Technol., Vol. 8, pp. 307–315, 1970.
Ishii, H., Representation of solutions of Hamilton–Jacobi equations, Nonlinear Anal. Theory, Meth. and Appl., Vol. 12, No. 2, pp. 121–146, 1988.
Ito, M., An extension of nonlinear evolution equations of the KdV (mKdV) type of higher orders, J. Phys. Soc. Japan, Vol. 49, pp. 771–778, 1980.
Its, A. R. and Novokshenov, V. Yu., The Isomonodromic Deformation Method in the Theory of Painleve Equations, Springer-Verlag, Berlin, 1986.
Ivanov, R., On the integrability of a class of nonlinear dispersive wave equations, J. Nonlin. Math. Phys., Vol. 12, No. 4, pp. 462–468, 2005.
Ivanov, R., Water waves and integrability, Phil. Trans. Roy. Soc. A, Vol. 365 (1858), pp. 2267–2280, 2007.
Ivanova, N. M., Exact solutions of diffusion-convection equations, Dynamics of PDEs, Vol. 5, No. 2, pp. 139–171, 2008.
Ivanova, N. M. and Sophocleous, C., On the group classification of variable coefficient nonlinear diffusion–convection equations, J. Comp. and Appl. Math., Vol. 197, pp. 322–344, 2006.
Ivlev, D. D., A class of solutions for general equations of ideal plasticity, Izvestiya AN S.S.S.R., Otdelenie Tekhnich. Nauk [in Russian], Vol. 11, p. 107, 1958.
Ivlev, D. D., Theory of Ideal Plasticity [in Russian], Nauka, Moscow, 1966.
Jacobs, D., McKinney, B., and Shearer, M., Travelling wave solutions of the modified Korteweg–de Vries–Burgers equation, J. Dif. Equations, Vol. 116, pp. 448–467, 1995.
Janke, E., Emde, F., and Losch, F., Tafeln Hoherer Funktionen, Teubner Verlogsgesellschaft, Stuttgart, 1960.
Jarai, A., Regularity Properties of Functional Equations in Several Variables, Springer-Verlag, New York, 2005.
Jeffrey, A., Quasilinear Hyperbolic Systems and Shock Waves, Pitman, London, 1976.
Jeffrey, A. and Xu, S., Exact solutions to the Korteweg–de Vries–Burgers equation, Wave Motion, Vol. 11, pp. 559–564, 1989.
Jeffery, G. B., The two-dimensional steady motion of a viscous fluid, Phil. Mag. Ser. 6, Vol. 9, pp. 455–465, 1915.
Jimbo, M., Kruskal, M. D., and Miwa, T., Painleve test for the self-dual Yang–Mills equation, Phys. Lett., Ser. A, Vol. 92, No. 2, pp. 59–60, 1982.
John, F., Partial Differential Equations, Springer-Verlag, New York, 1982.
Johnson, R. S., On the inverse scattering transform, the cylindrical Korteweg–de Vries equation and similarity solutions, Phys. Lett., Ser. A, Vol. 72, No. 2, p. 197, 1979.
Johnson, R. S., Camassa–Holm, Korteweg–de Vries and related models for water waves, J. Fluid Mech., Vol. 455, pp. 63–82, 2002.
Johnson, R. S., The classical problem of water waves: a reservoir of integrable and nearly-integrable equations, J. Nonlinear Math. Phys., Vol. 10 (Suppl. 1), pp. 72–92, 2003.
Kadomtsev, B. B. and Petviashvili, V. I., On the stability of solitary waves in a weak dispersion medium [in Russian], Doklady AN USSR, Vol. 192, No. 4, pp. 753–756, 1970.
Kaliappan, P., An exact solution for travelling waves of u_t=Du_xx+u−u^k, Physica D, Vol. 11, pp. 368–374, 1984.
Kambe, T., A class of exact solutions of two-dimensional viscous flow, J. Phys. Soc. Jpn., Vol. 52, pp. 834–841, 1983.
Kamke, E., Differentialgleichungen: Losungsmethoden und Losungen, II, Partielle Differentialgleichungen Erster Ordnung fur eine gesuchte Funktion, Akad. Verlagsgesellschaft Geest Portig, Leipzig, 1965.
Kamke, E., Differentialgleichungen: Losungsmethoden und Losungen, I, Gewohnliche Differentialgleichungen, B. G. Teubner, Leipzig, 1977.
Kaptsov, O. V., Steady-state vortex structures in ideal fluid, Zhur. eksperim. i teor. fiziki, Vol. 98, No. 2, pp. 532–541, 1990.
Kaptsov, O. V., Invariant sets of evolution equations, Nonlin. Anal., Vol. 19, pp. 753–761, 1992.
Kaptsov, O. V., Determining equations and differential constraints, Nonlinear Math. Phys., Vol. 2, No. 3-4, pp. 283–291, 1995.
Kaptsov, O. V., Construction of exact solutions of systems of diffusion equations, Mat. Model., Vol. 7, pp. 107–115, 1995.
Kaptsov, O. V., Linear determining equations for differential constraints, Sbornik: Mathematics, Vol. 189, pp. 1839–1854, 1998.
Kaptsov, O. V., Construction of exact solutions to the Boussinesq equation [in Russian], Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 39, No. 3, pp. 74–78, 1998.
Kaptsov, O. V., Integration Methods for Partial Differential Equations [in Russian], Fizmatlit, Moscow, 2009.
Kaptsov, O. V. and Shan'ko, Yu. V., Multiparameter solutions of the Tzitzeica equation [in Russian], Diff. Uravneniya, Vol. 35, No. 12, pp. 1660–1668, 1999.
Kaptsov, O. V. and Verevkin, I. V., Differential constraints and exact solutions of nonlinear diffusion equations, J. Phys. A: Math. Gen., Vol. 36, 1401–1414, 2003.
Kara, A. N. and Mahomed, F. M., A basis of conservation laws for partial differential equations, Nonlinear Math. Phys., Vol. 9, pp. 60–72, 2002.
von Karman, T., Encyklopedie der mathematischen Wissenschaften, Vol. 4, p. 349, 1910.
von Karman, T., Uber laminare und turbulente Reibung, Z. Angew. Math. Mech. (ZAMM), Vol. 1, pp. 233–252, 1921.
von Karman, T. and Howarth, L., On the statistical theory of isotropic turbulence, Proc. Roy. Soc., Vol. A164, pp. 192–215, 1938.
Katkov, V. L., Group invariant solutions for equations of breezes and monsoons, Meteorologia i hidrologia, Vol. 10, p. 11, 1964.
Katkov, V. L., Exact solutions of certain convection problems, Prikladn. Matematika i Mekhanika (PMM), 32, No. 3, p. 489, 1968.
Kaup, D., A higher-order water wave equation and the method for solving it, Prog. Theor. Phys., Vol. 54, pp. 396–408, 1975.
Kawahara, T., Oscillatory solitary waves in dispersive media, J. Phys. Soc. Japan, Vol. 33, No. 1, pp. 260–264, 1972.
Kawahara, T. and Tanaka, M., Interactions of traveling fronts: an exact solution of a nonlinear diffusion equations, Moscow Univ. Math. Bull., Vol. 33, p. 311, 1983.
Keller, H. B. and Szeto, R. K. H., Calculation of flows between rotating disks. In Computing Methods in Applied Sciences and Engineering (Eds. R. Glowinski and J. L. Lions), North Holland, Amsterdam, pp. 51–61, 1980.
Kelly, R. E., The flow of a viscous fluid past a wall of infinite extent with time-dependent suction, Quart. J. Mech. Appl. Math., Vol. 18, pp. 287–298, 1965.
Kersner, R., On the behaviour of temperature fronts in media with non-linear heat conductivity under absorption, Acta Math. Academy of Sciences, Hung., Vol. 32, pp. 35–41, 1978.
Kersner, R., Some properties of generalized solutions of quasilinear degenerate parabolic equations, Acta Math. Academy of Sciences, Hung., Vol. 32, No. 3–4, pp. 301–330, 1978.
Kevorkian, J., and Cole, J. D., Perturbation Methods in Applied Mathematics, Springer-Verlag, New York, 1981.
Khabirov, S. V., Lie pseudogroups of transformations on the plane and their differential invariants [in Russian], In: Modelling in Mechanics, SO AN USSR, Novosibirsk, Vol. 4 (21), No. 6, pp. 151–160, 1990.
Khabirov, S. V., Nonisentropic one-dimensional gas motions obtained with the help of the contact group of the nonhomogeneous Monge–Ampere equation [in Russian], Mat. Sbornik, Vol. 181, No. 12, pp. 1607–1622, 1990.
Khabirov, S. V., Application of contact transformations of the nonhomogeneous Monge–Ampere equation in one-dimensional gas dynamics [in Russian], Dokl. Acad. Nauk USSR, Vol. 310, No. 2, p. 333–336, 1990.
King, J. R., Mathematical analysis of a model for substitutional diffusion, Proc. Roy. Soc. London, Ser. A, Vol. 430, pp. 377–404, 1990.
King, J. R., Some non-local transformations between nonlinear diffusion equations, J. Phys. A: Math. Gen., Vol. 23, pp. 5441–5464, 1990.
King, J. R., Exact similarity solutions to some nonlinear diffusion equations, J. Phys. A: Math. Gen., Vol. 23, pp. 3681–3697, 1990.
King, J. R., Exact results for the nonlinear diffusion equations u_t = ( u^−4/3u_x)_x and u_t = ( u^−2/3u_x)_x, J. Phys. A: Math. Gen., Vol. 24, pp. 5721–5745, 1991.
King, J. R., Local transformations between some nonlinear diffusion equations, J. Aust. Math. Soc. B, Vol. 33, pp. 321–349, 1992.
King, J. R., Some non-self-similar solutions to a nonlinear diffusion equations, J. Phys. A: Math. Gen., Vol. 25, pp. 4861–4868, 1992.
King, J. R., Exact multidimensional solutions to some nonlinear diffusion equations, Quart. J. Mech. Appl. Math., Vol. 46, No. 3, pp. 419–436, 1993.
Kiryakov, P. P., Senashov, S. I., and Yakhno, A. N., Application of Symmetries and Conservation Laws to the Solution of Differential Equations, Izd-vo SO RAN, Novosibirsk, 2001.
Kivshar, Y., Compactons in discrete lattices, Nonlinear Coherent. Struct. Phys. Biol., Vol. 329, pp. 255–258, 1994.
Klimov, D. M., Baydulov, V. G., and Gorodtsov, V. A., The Kovalevskaya–Painleve test of the shallow water equations with the use of the Maple package, Doklady Mathematics, Vol. 63, No. 1, pp. 118–122, 2001.
Klimov, D. M. and Zhuravlev, V. Ph., Group-Theoretic Methods in Mechanics and Applied Mathematics, Taylor Francis, London, 2002.
Kochin, N. E., Kibel', I. A., and Roze, N. V., Theoretical Fluid Mechanics [in Russian], Fizmatgiz, Moscow, 1963. English translation: Interscience Publishers, New York, 1964.
Kodama, Y., A method for solving the dispersionless KP hierarchy and its exact solutions, Phys. Lett. A, Vol. 129, No. 4, pp. 223–226, 1988.
Kodama, Y. and Gibbons, J., A method for solving the dispersionless KP hierarchy and its exact solutions, II, Phys. Lett. A, Vol. 135, No. 3, pp. 167–170, 1989.
Kolmogorov, A. N., Petrovskii, I. G., and Piskunov, I. S., Investigation of the diffusion equation with increasing substance amount and application to a biological problem [in Russian], Byulleten' MGU, Sektsiya A, Vol. 1, No. 6, pp. 1–25, 1937.
Konopelchenko, B. G., Nonlinear Integrable Equations, Springer, New York, 1987.
Korepin, V. E., Bogoliubov, N. N., and Izergin A. G., Quantum Inverse Scattering Method and Correlation Functions, Cambridge Univ. Press, Cambridge, 1993.
Korn, G. A. and Korn, T. M., Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Comp., New York, 1961.
Korteweg, D. J. and Vries, G., On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Phil. Mag., Vol. 39, pp. 422–443, 1895.
Kosovtsov, Yu. N., The decomposition method and Maple procedure for finding first integrals of nonlinear PDEs of any order with any number of independent variables, 2007, arXiv: 0704.0072v1 [math-ph], 2007.
Kosovtsov, Yu. N., The general solutions of some nonlinear second-order PDEs. I. Two independent variables, constant parameters [online], arXiv.org: 0801.4081v1, 2008.
Kosovtsov, Yu. N., Plebanski first heavenly equation [online], EqArchive, 2008 (http://eqworld. ipmnet.ru/eqarchive/view.php?id=290).
Kosovtsov, Yu. N., Plebanski second heavenly equation [online], EqArchive, 2008 (http://eqworld. ipmnet.ru/eqarchive/view.php?id=334).
Koterov, V. N., Shmyglevskii, Yu. D., and Shcheprov, A. V., A survey of analytical studies of steady viscous incompressible flows (2000–2004), Comp. Math. Math. Phys., Vol. 45, No. 5, pp. 867–888, 2005.
Kovasznay, L. I. J., Laminar flow behind a two-dimensional grid, Proc. Cambridge Philos. Soc., Vol. 44, pp. 58–62, 1948.
Kozlov, V. F., Some exact solutions for the nonlinear equation of advection of density in Ocean, Izvestiya Akad. Nauk USSR, Fizika Atmosfery i Okeana, Vol. 2, p. 1205, 1966.
Kozlov, V. V., Symmetries, Topology and Resonances in Hamiltonian Mechanics [in Russian], Izd-vo Udmurtskogo Gos. Universiteta, Izhevsk, 1995.
Kreiss, H. O. and Parter, S. V., On the swirling flow between rotating coaxial disks: existence and nonuniqueness, Commun. Pure Appl. Math., Vol. 36, pp. 55–84, 1983.
Kreyszig, E., Maple Computer Guide for Advanced Engineering Mathematics, Wiley, New York, 8th ed., 2000.
Krichever, I. M., Analogue of D'Alembert's formula for main field equations and the sine-Gordon equation, Doklady AN USSR, Vol. 253, No. 2, pp. 288–292, 1980.
Krichever, I. M. and Novikov, S. P., Holomorphic bundles over Riemannian surfaces and the Kadomtsev–Petviashvili (KP) equation, Funkts. Analiz i ego Prilozh., Vol. 12, No. 4, pp. 41–52, 1978.
Krichever, I. M. and Novikov, S. P., Holomorphic bundles over algebraic curves and nonlinear equations, Russ. Math. Surv., Vol. 35, pp. 53–79, 1980.
Kruglikov, B., Symmetry approaches for reductions of PDEs, differential constraints and Lagrange–Charpit method, Acta Appl. Math., Vol. 101, pp. 145–161, 2008.
Kruskal, M. D., Miura, R. M., Gardner, C. S., and Zabusky, N. J., Korteweg–de Vries equation and generalizations. V. Uniqueness and nonexistence of polynomial conservation laws, J. Math. Phys., Vol. 11, pp. 952–960, 1970.
Kruzhkov, S. N., Generalized solutions of nonlinear first order equations with several variables [in Russian], Mat. Sbornik, Vol. 70, pp. 394–415, 1966.
Kruzhkov, S. N., Generalized solutions of Hamilton–Jacobi equations of the eikonal type [in Russian], Mat. Sbornik, Vol. 27, pp. 406–446, 1975.
Kucharczyk, P., Teoria Grup Liego w Zaslosowaniu do Rowman Rozniczkowych Czastkowych, IPPT Polish Academy of Sciences, Warsaw, 1967.
Kuczma, M., An Introduction to the Theory of Functional Equations and Inequalities, Polish Scientific Publishers, Warsaw, 1985.
Kudryashov, N. A., Exact soliton solutions of the generalized evolution equation of wave dynamics, J. Appl. Math. and Mech., Vol. 52, No. 3, pp. 360–365, 1988.
Kudryashov, N. A., Exact solutions of an Nth-order equation with a Burgers–Korteweg–de Vries type nonlinearity [in Russian], Mat. Modelirovanie, Vol. 1, No. 6, pp. 57–65, 1989.
Kudryashov, N. A., Exact solutions of nonlinear wave equations arising in mechanics, Appl. Math. and Mech. (PMM), Vol. 54, No. 3, pp. 450–453, 1990.
Kudryashov, N. A., Exact solutions of the generalized Kuramoto–Sivashinsky equation, Phys. Lett. A, Vol. 147, No. 5–6, pp. 287–291, 1990.
Kudryashov, N. A., On types of nonlinear nonintegrable solutions with exact solutions, Phys. Lett. A, Vol. 155, No. 4–5, pp. 269–275, 1991.
Kudryashov, N. A., On exact solutions of families of Fisher equations, Theor. Math. Phys., Vol. 94, No. 2, pp. 211–218, 1993.
Kudryashov, N. A., Symmetry of algebraic and differential equations. Soros Educational Journal [in Russian], No. 9, pp. 104–110, 1998.
Kudryashov, N. A., Nonlinear differential equations with exact solutions expressed via the Weierstrass function, Zeitschrift fur Naturforschung, Vol. 59, pp. 443–454, 2004.
Kudryashov, N. A., Analytical Theory of Nonlinear Differential Equations [in Russian], Institut kompjuternyh issledovanii, Moscow–Izhevsk, 2004.
Kudryashov, N. A., Simplest equation method to look for exact solutions of nonlinear differential equations, Chaos, Solitons and Fractals, Vol. 24, No. 5, pp. 1217–1231, 2005.
Kudryashov, N. A., On "new travelling wave solutions" of the KdV and the KdV–Burgers equations, Commun. Nonlinear Sci. and Numer. Simulation, Vol. 14, No. 5, pp. 1891–1900, 2009.
Kudryashov, N. A., Seven common errors in finding exact solutions of nonlinear differential equations, Commun. Nonlinear Sci. and Numer. Simulation, Vol. 14, No. 9–10, pp. 3507–3529, 2009.
Kudryashov, N. A., Comment on: "A novel approach for solving the Fisher equation using Exp-function method" [Phys. Lett. A, Vol. 372 pp. 3836–3840, 2008], Physics Letters A, Vol. 373, No. 12–13, pp. 1196–1197, 2009.
Kudryashov, N. A., A note on new exact solutions for the Kawahara equation using Exp-function method, J. Comp. Appl. Math., Vol. 234, No. 12, pp. 3511–3512, 2010.
Kudryashov, N. A., A note on the G'/G-expansion method, Appl. Math. Comp., Vol. 217, No. 4, pp. 1755–1758, 2010.
Kudryashov, N. A., A new note on exact complex travelling wave solutions for (2+1)-dimensional B-type Kadomtsev–Petviashvili equation, Appl. Math. Comp., Vol. 217, No. 5, pp. 2282–2284, 2010.
Kudryashov, N. A., Methods of Nonlinear Mathematical Physics [in Russian], Izd. Dom Intellekt, Dolgoprudnyi, 2010.
Kudryashov, N. A., On completely integrability systems of differential equations, Commun. Nonlinear Sci. and Numer. Simulation, Vol. 16, No. 6, pp. 2414–2420, 2011.
Kudryashov, N. A., Redundant exact solutions of nonlinear differential equations, Commun. Nonlinear Sci. and Numer. Simulations, Vol. 16, No. 9, pp. 3451–3456, 2011.
Kudryashov, N. A. and Loguinova, N. B., Extended simplest equation method for nonlinear differential equations, Applied Mathematics and Computation, Vol. 205, No. 1, pp. 396-402, 2008.
Kudryashov, N. A. and Loguinova, N. B., Be careful with the Exp-function method, Commun. Nonlinear Sci. and Numer. Simulation, Vol. 14, No. 5, pp. 1881–1890, 2009.
Kudryashov, N. A., Ryabov, P. N., and Sinelshchikov, D. I., A note on "New kink-shaped solutions and periodic wave solutions for the (2+1)-dimensional sine–Gordon equation," Appl. Math. Comp., Vol. 216, No. 8, pp. 2479–2481, 2010.
Kudryashov, N. A., Ryabov, P. N., and Sinelshchikov, D. I., Comment on: ``Application of the (G'/G) method for the complex KdV equation'' [Zhang, H., Commun. Nonlinear Sci. Numer. Simulation, Vol. 15, pp. 1700–1704, 2010], Commun. Nonlinear Sci. Numer. Simulation, Vol. 16, No. 1, pp. 596–598, 2011.
Kudryashov, N. A. and Sinelshchikov, D. I., A note on "Abundant new exact solutions for the (3+1)-dimensional Jimbo–Miwa equation," J. Math. Anal. Appl., Vol. 371, No. 1, pp. 393–396, 2010.
Kudryashov, N. A. and Soukharev, M. B., Exact solutions of a non-linear fifth-order equation for describing waves on water, Appl. Math. and Mech. (PMM), Vol. 65, No. 5, pp. 855–865, 2001.
Kudryashov, N. A. and Soukharev, M. B., Popular ansatz methods and solitary waves solutions of the Kuramoto–Sivashinsky equation, Regular and Chaotic Dynamics, Vol. 14, No. 3, pp. 407–419, 2009.
Kudryashov, N. A. and Soukharev, M. B., Comment on: "Multi soliton solution, rational solution of the Boussinesq–Burgers equations," Commun. Nonlinear Sci. and Numer. Simulation, Vol. 15, No. 7, pp. 1765–1767, 2010.
Kulikovskii, A. G., Properties of shock adiabats in the neighbourhood of Jouguet points, Fluid Dynamics, Vol. 14, No. 2, pp. 317-320, 1979.
Kulikovskii, A. G. and Sveshnikova, E. I., Nonlinear Waves in Elastic Media, CRC Press, Boca Raton, 1995.
Kulikovskii, A. G., Pogorelov, N. V., and Semenov, A. Yu., Mathematical Aspects of Numerical Solution of Hyperbolic Systems, Chapman Hall/CRC Press, Boca Raton, 2001.
Kumar, S. N. and Panigrahi, P. K., Compacton-like solutions for KdV and other nonlinear equations, REVTEX electr. manusct., 23 April 1999.
Kupershmidt, B. A., A super KdV equation: An integrable system, Phys. Letters, Vol. 102 A, pp. 212–215, 1984.
Kuramoto, Y. and Tsuzuki, T., On the formation of dissipative structures in reaction-diffusion systems, Progr. Theor. Phys., Vol. 54, No. 3, pp. 687–699, 1975.
Kuramoto, Y. and Tsuzuki, T., Persistent propagation of concentration waves in dissipative media from thermal equilibrium, Progr. Theor. Phys., Vol. 55, No. 2, pp. 356–369, 1976.
Kuranishi, M., Lectures on Involutive Systems on Partial Differential Equations, Publ. Soc. Math., Sao Paulo, 1967.
Kurenskii, M. G., Differential Equations. Book Two: Partial Differential Equations [in Russian], Izd-vo Artilleriiskoi Akad. RKKA, Leningrad, 1934.
Kuznetsov, N. N., Some mathematical problems of chromatography, Vychisl. Metody i Progr. [in Russian], Moscow State Univ., Vol. 6, pp. 242–258, 1967.
Lagerstrom, P. A., Laminar Flow Theory, Princeton Univ. Press, Princeton, NJ, 1996 [Originally published in Theory of Laminar Flows (Ed. F. K. Moore), Princeton Univ. Press, Princeton, NJ, 1964].
Lagerstrom, P. A. and Cole, J. D., Examples illustrating expansion procedures for the Navier–Stokes equations, J. Rat. Mech. Anal., Vol. 4, pp. 817–882, 1955.
Lagno, V. I. and Stognii, V. I., Symmetric reduction of a nonlinear Kolmogorov-type equation and group classification of one of its generalizations, In: Some Topical Problems of Modern Mathematics and Mathematical Education (Ed. V. F. Zaitsev) [in Russian], Saint-Petersburg, pp. 42–44, 2010.
Lai, C.-Y., Rajagopal, K. R., and Szeri, A. Z., Asymmetric flow between parallel rotating disks, J. Fluid Mech., Vol. 446, pp. 203–225, 1984.
Lake, L. W., Enhanced Oil Recovery, Prentice Hall, Eaglewood Cliffs, N.J., 1989.
Lamb, G. L., Analytical descriptions of ultrashort optical pulse propagation in a resonant medium, Rev. Mod. Phys., Vol. 43, pp. 99–124, 1971.
Lamb, G. L., Backlund transformations for certain nonlinear evolution equations, J. Math. Phys., Vol. 15, pp. 2157–2165, 1974.
Lamb, G. L., Elements of Soliton Theory, Wiley, New York, 1980.
Lamb, H., Hydrodynamics, Dover Publ., New York, 1945.
Lambossy, P., Oscillations forcees dun liquide incompressible et visqueux dans un tube rigide et horizontal. Calcul de la force de frottement, Helv. Phys. Acta, Vol. 25, pp. 371–386, 1952.
Lan, H. and Wang, K., Exact solutions for some nonlinear equations, Phys. Lett., Vol. 139, No. 7–8, pp. 369–372, 1989.
Lance, G. N. and Rogers, M. H., The axially symmetric flow of a viscous fluid between two infinite rotating disks, Proc. Roy. Soc. London, Ser. A, Vol. 266, pp. 109–121, 1962.
Landau, L. D., Dokl. Acad. Nauk USSR, Vol. 43, p. 286, 1944.
Landau, L. D. and Lifshitz, E. M., Fluid Mechanics, 3rd ed. [in Russian], Nauka, Moscow, 1986; 2nd English ed., Pergamon Press, Oxford, 1987.
Lapidus, L. and Pinder, G. F., Numerical Solution of Partial Differential Equations in Science and Engineering, Wiley-Interscience, New York, 1999.
Lapko, B. V., Invariant solutions of three-dimensional nonstationary gas motion, Zh. Prikl. Mekh. Tekh. Fiz., No. 1, p. 45, 1978.
Larsson, S. and Thomee, V., Partial Differential Equations with Numerical Methods, Springer, New York, 2008.
Lavrent'ev, M. A. and Shabat, B. V., Methods of the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow, 1973.
Lavrent'eva, O. M., Flow of a viscous fluid in a layer on a rotating fluid, J. Appl. Mech. Tech. Phys., No. 5, pp. 41–48, 1989.
Lawrence, C. J., Kuang, Y., and Weinbaum, S., The inertial draining of a thin fluid layer between parallel plates with a constant normal force. Part 2. Boundary layer and exact numerical solutions, J. Fluid Mech., Vol. 156, pp. 479–494, 1985.
Lax, P. D., Weak solutions of nonlinear hyperbolic equations and their numerical computation, Communs. Pure and Appl. Math., Vol. 7, pp. 159–193, 1954.
Lax, P. D., Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math., Vol. 21, No. 5, pp. 467–490, 1968.
Lax, P. D., Periodic solutions of the KdV equation, Comm. Pure Appl. Math., Vol. 28, pp. 144–188, 1975.
Lax, P. D., Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves [reprint from the classical paper of 1957], Society of Industrial Applied Mathematics, Philadelphia, 1997.
Lee, H. J. and Schiesser, W. E., Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple, and MATLAB, Chapman Hall/CRC Press, Boca Raton, 2004.
Lei, H. C., Group splitting and linearization mapping of a solvable nonlinear wave equation, Int. J. Non-Linear Mechanics, Vol. 33, pp. 461–471, 1998.
Lei, H. C., Study of a hodograph transformation and its applications, J. Chinese Inst. Engineers, Vol. 25, No. 6, pp. 77–714, 2002.
Lei, H. C. and Chang, H. W., A list of hodograph transformations and exactly linearizable systems, Int. J. Non-Linear Mechanics, Vol. 31, pp. 117–127, 1996.
Lenells, J., Traveling wave solutions of the Camassa–Holm equation, J. Dif. Equations, Vol. 217, No. 2, pp. 393–430, 2005.
Lenells, J., Traveling wave solutions of the Degasperis–Procesi equation, J. Math. Anal. Appl., Vol. 306, No. 1, pp. 72–82, 2005.
Lenells, J., The Hunter–Saxton equation describes the geodesic flow on a sphere, J. Geom. Phys., Vol. 57, No. 10, pp. 2049–2064, 2007.
Lenskii, E. V., On the group properties of the equation of motion of a nonlinear viscoplastic medium, Vestnik MGU, Ser. 1 (Math. i Meh.), pp. 116–125, 1966.
Leo, M., Leo, R. A., Soliani, G., Solombrino, L., and Martina, L., Lie–Backlund symmetries for the Harry Dym equation, Phys. Rev. D., Vol. 27, No. 6, pp. 1406–1408, 1983.
LeVeque, R. J., Numerical Methods for Conservation Laws, Birkhauser, Boston, 1992.
LeVeque, R. J., Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge, 2002.
LeVeque, R. J., Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, SIAM, Philadelphia, 2007.
Levi, D., Petrera, M., and Scimiterna, C., The lattice Schwarzian KdV equation and its symmetries, J. Phys. A: Math. Theor., Vol. 40, pp. 12753–12761, 2007.
Levi, D. and Winternitz, P., Nonclassical symmetry reduction: example of the Boussinesq equation, J. Phys. A, Vol. 22, pp. 2915–2924, 1989.
Levitan, B. M., Sturm–Liouville Inverse Problems [in Russian], Nauka, Moscow, 1984.
Lewin, J., Differential Games, Springer-Verlag, Berlin, 1994.
Libby, P. A., Heat and mass transfer at a general three-dimensional stagnation point with large rates of injection, AIAA J., Vol. 5, pp. 507–517, 1967.
Libby, P. A., Wall shear at a three-dimensional stagnation point with a moving wall, AIAA J., Vol. 14, pp. 1273–1279, 1974.
Libby, P. A., Laminar flow at a three-dimensional stagnation point with large rates of injection, AIAA J., Vol. 12, pp. 408–409, 1976.
Liebbrandt, G., New exact solutions of the classical sine-Gordon equation in 2+1 and 3+1 dimensions, Phys. Rev. Lett., Vol. 41, pp. 435–438, 1978.
Lighthill, J., Waves in Fluids, Cambridge Univer. Press, Cambridge, 1978.
Lin, C. C., Note on a class of exact solutions in magneto-hydrodynamics, Arch. Rational Mech. Anal., Vol. 1, pp. 391–395, 1958.
Lin, C. C., Reissner, E., and Tsien, H. S., On two-dimensional non-steady motion of a slender body in a compressible fluid, J. Math. Phys., Vol. 27, No. 3, p. 220, 1948.
Lin, S. P. and Tobak, M., Reversed flow above a plate with suction, AIAA J., Vol. 24, pp. 334–335, 1986.
Lindsay, R. B., J. L. R. d'Alembert, Investigation of the curve formed by a vibrating string, In: Acoustics: Historical and Philosophical Development, Dowden, Hutchinson Ross, Stroudsburgh, PA, 1973.
Lineikin, P. S., Hydrodynamical models of nonhomogeneous ocean, Okeanologia, Vol. 3, p. 369, 1963.
Lions, P.-L., Generalized Solutions of Hamilton–Jacobi Equations, Pitman, Boston, 1982.
Lions, P.-L. and Souganidis, P. E., Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Isaacs' solutions, SIAM J. Control and Optimization, Vol. 23, No. 4, 1985.
Liouville, J., Sur l'equation aux differences partielles: (log λ)_uv+αλ=0, J. Math., Vol. 18, pp. 71–72, 1853.
Litvinenko, Yu. E., A similarity reduction of the Grad–Shafranov equation, Phys. Plasmas, Vol. 17, 074502, 2010 (doi:10.1063/1.3456519).
Liu, T. P., The Riemann problem for general 2x2 system of conservation laws, Trans. Amer. Math. Soc., Vol. 199, pp. 89–112, 1974.
Lloyd, S. P., The infinitesimal group of the Navier–Stokes equations, Acta Mech., Vol. 38, pp. 85–98, 1981.
Logan, D. J., Nonlinear Partial Differential Equations, John Wiley Sons Inc., New York, 1994.
Loitsyanskiy, L. G., Mechanics of Liquids and Gases, Begell House, New York, 1996.
Long, R. R., Vortex motion in a viscous fluid, J. Meteotol., Vol. 15, pp. 108–112, 1958.
Long, R. R., A vortex in an infinite viscous fluid, J. Fluid Mech., Vol. 11, pp. 611–624, 1961.
Lonngren, K. and Scott, A. (Eds.), Solitons in Action, Academic Press, New York, 1978.
Loubet, E., About the explicit characterization of Hamiltonians of the Camassa–Holm hierarchy, J. Nonlinear Math. Phys., Vol. 12, No. 1, pp. 135–143, 2005.
Ludford, C. S., Generalized Riemann invariants, Pacif. J. Math., Vol. 5, pp. 441–450, 1955.
Ludlow, D. K., Clarkson, P. A., and Bassom, A. P., Nonclassical symmetry reductions of the two-dimensional incompressible Navier–Stokes equations, Studies in Applied Mathematics, Vol. 103, pp. 183–240, 1999.
Ludlow, D. K., Clarkson, P. A., and Bassom, A. P., New similarity solutions of the unsteady incompressible boundary-layer equations, Quart. J. Mech. and Appl. Math., Vol. 53, pp. 175–206, 2000.
Lundmark, H., Formation and dynamics of shock waves in the Degasperis–Procesi equation, J. Nonlinear Sci., Vol. 17, No. 3, pp. 169–198, 2007.
Lundmark, H. and Szmigielski, J., Multi-peakon solutions of the Degasperis–Procesi equation, Inverse Problems, Vol. 19, No. 6, pp. 1241–1245, 2003.
Lykov, A. V., Theory of Heat Conduction [in Russian], Vysshaya Shkola, Moscow, 1967.
Lynch, S., Dynamical Systems with Applications using Maple, Birkhauser, Boston, MA, 2nd ed., 2009.
Ma, P. K. H. and Hui, W. H., Similarity solutions of the two-dimensional unsteady boundary-layer equations J. Fluid Mech., Vol. 216, pp. 537–559, 1990.
Ma, W.-X., Travelling wave solutions to a seventh order generalized KdV equation, Phys. Lett. A, Vol. 180, 221–224, 1993.
Ma, W.-X. and You, Y., Solving the Korteweg–de Vries equation by its bilinear form: Wronskian solutions, Trans. Amer. Math. Soc., Vol. 357, pp. 1753–1778, 2005.
Macias, A., Cervantes-Cota, J. L., and Lammerzahl, C. (Eds.), Exact Solutions and Scalar Fields in Gravity, Springer, 2001.
Maeder, R. E., Programming in Mathematica, Addison-Wesley, Reading, MA, 3rd ed., 1996.
Malfliet, W., Solitary wave solutions of nonlinear wave equations, Am. J. Phys., Vol. 60, No. 7, pp. 650–654, 1992.
Malfliet, W. and Hereman, W., The tanh method: exact solutions of nonlinear evolution and wave equations, Phys Scripta, Vol. 54, pp. 563–568, 1996.
Mamontov, E. V., To the theory of unsteady transonic flows [in Russian], Doklady AN USSR, Vol. 185, No. 3, pp. 538–540, 1969.
Mansfield, E. H., Quart. J. Mech. Appl. Math., Vol. 8, p. 338, 1955.
Mansfield, E. L., The nonclassical group analysis of the heat equation, J. Math. Anal. Appl., Vol. 231, pp. 526–542, 1999.
Marchenko, A. V., Long waves in shallow liquid under ice cover, Appl. Math. and Mech. (PMM), Vol. 52, No. 2, pp. 180–183, 1988.
Marchenko, V. A., Sturm–Liouville Operators and Applications, Birkhauser, Basel, 1986.
Marino, K., Ankiewicz, A., and Akhmediev, N., Exact soliton solutions of the one-dimensional complex Swift–Hohenberg equation, Physica D, Vol. 176, pp. 44–66, 2003.
Markeev, A. P., Theoretical Mechanics [in Russian], Nauka, Moscow, 1990.
Martin, M. N., The propagation of a plane shock into a quiet atmosphere, Canad. J. Math., Vol. 3, pp. 165–187, 1953.
Mart\'inez, A. L. and Shabat, A. B., Towards a theory of differential constraints of a hydrodynamic hierarchy, J. Nonlin. Math. Phys., Vol. 10, pp. 229–242, 2003.
Martinson, L. K., Plane problem of convective heat transfer in a nonlinear medium, Appl. Math. and Mech. (PMM), Vol. 44, No. 1, pp. 128–131, 1980.
Martinson, L. K. and Pavlov, K. B., To the question of space localization of thermal perturbations in nonlinear heat conduction theory [in Russian], Zhurn. Vychisl. Matem. i Matem. Fiziki, Vol. 12, No. 4, pp. 1048–1054, 1972.
Matsuno, Y., Exact solutions for the nonlinear Klein–Gordon and Liouville equations in four-dimensional Euclidean space, J. Math. Physics, Vol. 28, No. 10, pp. 2317–2322, 1987.
Matsuno, Y., The N-soliton solution of the Degasperis–Procesi equation, Inverse Problems, Vol. 21, No. 6, pp. 2085–2101, 2005.
McKean, H. P., The Liouville correspondence between the Korteweg–de Vries and the Camassa–Holm hierarchies, Comm. Pure Appl. Math., Vol. 56, No. 7, 998–1015, 2003.
McLeod, J. B., The existence of axially symmetric flow above a rotating disk, Proc. Roy. Soc. London, Ser. A, Vol. 324, pp. 391–414, 1971.
McLeod, J. B. and Parter, S. V., On the flow between two counter-rotating infinite plane disks, Arch. Rat. Mech. Anal., Vol. 42, pp. 385–327, 1974.
Meade, D. B., May, S. J. M., Cheung, C-K., and Keough, G. E., Getting Statrted with Maple, Wiley, Hoboken, NJ, 3rd ed., 2009.
Meirmanov, A. M., Pukhnachov, V. V., and Shmarev, S. I., Evolution Equations and Lagrangian Coordinates, Walter de Gruyter, Berlin, 1997.
Meleshko, S. V., Differential constraints and one-parameter Lie–Backlund groups, Sov. Math. Dokl., Vol. 28, pp. 37–41, 1983.
Meleshko, S. V., A particular class of partially invariant solutions of the Navier–Stokes equations, Nonlinear Dynamics, Vol. 36. No. 1, pp. 47–68, 2004.
Meleshko, S. V., Methods for Constructing Exact Solutions of Partial Differential Equations, Springer-Verlag, New York, 2005.
Meleshko, S. V. and Pukhnachov, V. V., A class of partially invariant solutions of Navier–Stokes equations, J. Appl. Mech. Tech. Phys., Vol. 40, No. 2, pp. 24–33, 1999.
Melikyan, A. A., Singular characteristics of the first order PDEs, Doklady Mathematics, Vol. 54, No. 3, pp. 831–834, 1996.
Melikyan, A. A., Generalized Characteristics of First Order PDE's: Applications in Optimal Control and Differential Games, Birkhauser, Boston, 1998.
Melor, G. L., Chapple, P. J., and Stokes, V. K., On the flow between a rotating and a stationary disk, Fluid Mech., Vol. 31, pp. 95–112, 1968.
Mel'nikov, V. K., Structure of equations solvable by the inverse scattering transform for the Schrodinger operator, Theor. Math. Phys., Vol. 134, No. 1, pp. 94–106, 2003.
Menshikh, O. F., On group properties on nonlinear partial differential equations whose solutions are all functionally invariant, Vestnik Samarskogo Gos. Universiteta [in Russian], No. 4 (34), pp. 20–30, 2004.
Menshikov, V. M., Solutions of two-dimentional gasdynamics equations of the simple wave type, Zh. Prikl. Mekh. Tekh. Fiz., Vol. 3, p. 129, 1969.
Merchant, G. I. and Davis, S. H., Modulated stagnation-point flow and steady streaming, J. Fluid Mech., Vol. 198, pp. 543–555, 1989.
Meshcheryakova, E. Yu., New steady and self-similar solutions of the Euler equations, J. Appl. Mech. Tech. Phys., Vol. 44, pp. 455–460, 2003.
Mikhailov, A. V., On the integrability of the two-dimensional generalization of Tod's chain [in Russian], Pis'ma v ZhETF, Vol. 30, No. 7, pp. 443–448, 1979.
Mikhailov, A. V., Shabat, A. B., and Sokolov, V. V., The symmetry approach to classification of integrable equations, In: What is Integrability? (Ed. V. E. Zakharov), pp. 115–184, Springer-Verlag, 1991.
Miller, W. (Jr.) and Rubel, L. A., Functional separation of variables for Laplace equations in two dimensions, J. Phys. A, Vol. 26, pp. 1901–1913, 1993.
Millsaps, K. and Pohlhausen, K., Thermal distributions in Jeffery–Hamel flows between nonparallel plane walls, J. Aerosp. Sci., Vol. 20, pp. 187–196, 1953.
Mironov, A. N., Construction of a exact solution to one quasilinear partial differential equation with three independent variables, In: Some Topical Problems of Modern Mathematics and Mathematical Education (Ed. V. F. Zaitsev) [in Russian], Saint-Petersburg, pp. 66–68, 2010.
Miura, R. M., Korteweg–de Vries equation and generalizations. I. A remarkable explicit nonlinear transformation, J. Math. Phys., Vol. 9, No. 8, pp. 1202–1204, 1968.
Miura, R. M., In: Nonlinear waves (Eds. S. Leibovich and A. R. Seebass), Cornell Univ. Press, Ithaca London, 1974.
Miura, R. M. (Ed.), Backlund Transformations, Lecture Notes in Math., Vol. 515, Springer-Verlag, Berlin, 1976.
Miura, R. M., Gardner, C. S., and Kruskal, M. D., Korteweg–de Vries equation and generalizations. II. Existence of conservation laws and constants of motion, J. Math. Phys., Vol. 9, pp. 1204–1209, 1968.
Miwa, T., Jimbo, M., and Date, E., Solitons. Differential Equations, Symmetries and Infinite-Dimensional Algebras, Cambridge Univ. Press, Cambridge, 2000.
Moffat, H. K., The interaction of skewed vortex pairs: a model for blow-up of the Navier–Stokes equations, J. Fluid Mech., Vol. 409, pp. 51–68, 2000.
Moore, R. L., Exact non-linear forced periodic solutions of the Navier–Stokes equations, Physica D, Vol. 52, pp. 179–190, 1991.
Morton, K. W. and Mayers, D. F., Numerical Solution of Partial Differential Equations: An Introduction, Cambridge University Press, Cambridge, 1995.
Muller, W., Zum Problem der Anlanfstromung einer Flussigkeit im geraden Rohr mit Kreisring- und Kreisquerschnitt, Zs. Angew Math. Mech. (ZAMM), Bd. 16, Ht. 4, S. 227–238, 1936.
Munier, A., Burgan, J. R., Gutierres, J., Fijalkow, E., and Feix M. R., Group transformations and the nonlinear heat diffusion equation, SIAM J. Appl. Math., Vol. 40, No. 2, pp. 191–207, 1981.
Murphy, G. M., Ordinary Differential Equations and Their Solutions, D. Van Nostrand, New York, 1960.
Murray, J. D., Mathematical Biology, Springer-Verlag, Berlin, 1993.
Musette, M., Painleve analysis for nonlinear partial differential equations, pp. 1–48, In: The Painleve Property, One Century Later (Ed. R. Conte), CRM Series in Math. Phys, Springer-Verlag, Berlin, 1998.
Musette, M. and Conte, R., Algorithmic method for deriving Lax pairs from the invariant Painleve analysis of nonlinear partial differential equations, J. Math. Phys., Vol. 32, No. 6, pp. 1450–1457, 1991.
Musette, M. and Conte, R., The two-singular-manifold method: Modified Korteweg–de Vries and the sine-Gordon equations, Phys. A, Math. Gen., Vol. 27, No. 11, pp. 3895–3913, 1994.
Nariboli, G.A., Self-similar solutions of some nonlinear equations, Appl. Sci. Res., Vol. 22, pp. 449–461, 1970.
Navier, C.-L.-M.-H., Memoire sur les lois du mouvement des fluids (1822), Mem. Acad. Sci. Inst. France, Vol. 6, No. 2, pp. 389–440, 1827.
Nayfeh, A. H., Perturbation Methods, John Wiley Sons, New York, 1973.
Nechepurenko, M. I., Iterations of Real Functions and Functional Equations [in Russian], Institute of Computational Mathematics and Mathematical Geophysics, Novosibirsk, 1997.
Nerney, S., Schmahl, E. J., and Musielak Z. E., Analytic solutions of the vector Burgers' equation, Quart. Appl. Math., Vol. LIV, No. 1, pp. 63–71, 1996.
Nesterov, S. V., Examples of nonlinear Klein–Gordon equations solvable in terms of elementary functions [in Russian], pp. 68–70, In: Applied Issues of Mathematics, Mosk. Energeticheskii Institut, Moscow, 1978.
Newell, A. C., Solitons in Mathematics and Physics, Soc. Indus. Appl. Math. (SIAM), Arizona, 1985.
Newman, W. I., Some exact solutions to a nonlinear diffusion problem in population genetics and combustion, J. Theor. Biol., Vol. 85, pp. 325–334, 1980.
Neyzi, F., Nutku, Y., and Sheftel, M. B., Multi-Hamiltonian structure of Plebanski's second heavenly equation, J. Phys. A: Math. Gen., Vol. 38, No. 39, pp. 8473–8485, 2005.
Nigmatulin, R. I., Dynamics of Multiphase Media, Part I [in Russian], Nauka, Moscow, 1987.
Nijenhuis, A., X _n-1-forming sets of eigenvectors, Indagationes Mathematicae, Vol. 13, No. 2, pp. 200–212, 1951.
Nikitin, A. G., Group classification of systems of non-linear reaction-diffusion equations with general diffusion matrix. II. Generalized Turing systems, J. Math. Anal. Appl., Vol. 332, No. 1, pp. 666–690, 2007.
Nikitin, A. G. and Wiltshire, R. J., Systems of reaction-diffusion equations and their symmetry properties, J. Math. Phys., Vol. 42, No. 4, pp. 1667–1688, 2001.
Nimmo, J. J. C. and Crighton, D. J., Backlund transformations for nonlinear parabolic equations: the general results. Proc. Royal Soc. London A, 1982, Vol. 384, pp. 381–401.
Nishitani, T. and Tajiri, M., On similarity solutions of the Boussinesq equation, Phys. Lett. A, Vol. 89, pp. 379–380, 1982.
Novikov, S. P., A periodic problem for the Korteweg–de Vries equation [in Russian], Funkts. Analiz i ego Prilozh., Vol. 8, No. 3, pp. 54–66, 1974.
Novikov, S. P., Manakov, S. V., Pitaevskii, L. B., and Zakharov, V. E., Theory of Solitons. The Inverse Scattering Method, Plenum Press, New York, 1984.
Nucci, M. C. and Clarkson, P. A., The nonclassical method is more general than the direct method for symmetry reductions. An example of the Fitzhugh–Nagumo equation, Phys. Lett. A, Vol. 164, pp. 49–56, 1992.
Oberlack, M. and Peters, N., Closure of the two-point correlation equation as a basis for Reynolds stress models, Appl. Sci. Res., Vol. 55, pp. 533–538, 1993.
O'Brien, V., Steady spheroidal vortices – more exact solutions to the Navier–Stokes equations, Quart. Appl. Math., Vol. 19, pp. 163–168, 1961.
Ockendon, H., An asymptotic solution for steady flow above an infinite rotating disk with suction, Quart. J. Mech. Appl. Math., Vol. 25, pp. 291–301, 1972.
Okamura, M., Resonant standing waves on water of uniform depth, J. Phys. Soc. Jpn., Vol. 66, pp. 3801–3808, 1997.
Oleinik, O. A., On Cauchy's problem for nonlinear equations in the class of discontinuous functions [in Russian], Doklady AN USSR, Vol. 95, No. 3, pp. 451–454, 1954.
Oleinik, O. A., Discontinuous solutions of nonlinear differential equations, Uspekhi Matem. Nauk, Vol. 12, No. 3, pp. 3–73, 1957 [Amer. Math. Soc. Translation, Series 2, Vol. 26, pp. 95–172, 1963].
Oleinik, O. A., On uniqueness and stability of a general solution of Cauchy's problem of quasilinear equations [in Russian], Uspekhi Matem. Nauk, Vol. 14, No. 2, pp. 159–164, 1959.
Oleinik, O. A. and Samokhin, V. N., Mathematical Models in Boundary Layer Theory, Chapman Hall/CRC Press, Boca Raton, 1999.
Olver, P. J., Euler operators and conservation laws of the BBM equation, Math. Proc. Camb. Phil. Soc., Vol. 85, pp. 143–160, 1979.
Olver, P. J., Hamilton and non-Hamilton models for water waves, Lecture Notes in Physics, Springer-Verlag, New York, No. 195, pp. 273–290, 1984.
Olver, P. J., Application of Lie Groups to Differential Equations, Springer-Verlag, New York, 1986 and 1993.
Olver, P. J., Direct reduction and differential constraints, Proc. Roy. Soc. London, Ser. A, Vol. 444, pp. 509–523, 1994.
Olver, P. J., Equivalence, Invariants, and Symmetry, Cambridge Univ. Press, Cambridge, 1995.
Olver, P. J., Classical Invariant Theory, Cambridge Univ. Press, Cambridge, 1999.
Olver, P. J. and Rosenau, P., The construction of special solutions to partial differential equations, Phys. Letters A, Vol. 114, pp. 107–112, 1986.
Olver, P. J. and Rosenau, P., Group-invariant solutions of differential equations, SIAM J. Appl. Math., Vol. 47, No. 2, pp. 263–278, 1987.
Olver P. J., and Vorob'ev E. M., Nonclassical and conditional symmetries, In: CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 3 (Ed. N. H. Ibragimov), CRC Press, Boca Raton, 1996, pp. 291–328.
Ono, H., Algebraic soliton of the modified Korteweg–de Vries' equation, J. Soc. Japan, Vol. 41, pp. 1817–1818, 1976.
Oron, A. and Rosenau, P., Some symmetries of nonlinear heat and wave equations, Phys. Letters A, Vol. 118, pp. 172–176, 1986.
Oseen, C. W., Uber Wirbelbewegung in einer reibenden Flussigkeit, Ark. Mat. Astron. Fys., Vol. 7, pp. 14–26, 1911.
Ovsiannikov, L. V., New solution of hydrodynamics equations, Doklady Acad. Nauk USSR, Vol. 111, No. 1, p. 47, 1956.
Ovsiannikov, L. V., Group properties of nonlinear heat equations [in Russian], Doklady Acad. Nauk USSR, Vol. 125, No. 3, pp. 492–495, 1959.
Ovsiannikov, L. V., Group Properties of Differential Equations [in Russian], Izd-vo SO AN USSR, Novosibirsk, 1962 (English translation by G. Bluman, 1967).
Ovsiannikov, L. V., Lectures on Fundamentals of Gas Dynamics [in Russian], Nauka, Moscow, 1981.
Ovsiannikov, L. V., Group Analysis of Differential Equations, Academic Press, New York, 1982.
Oztekin, A., Seymour, B. R., and Varley, E., Pump flow solutions of the Navier–Stokes equations, Stud. Appl. Math., Vol. 107, pp. 1–41, 2001.
Palais, R. S., The symmetries of solitons, Bull. AMS, Vol. 34, No. 4, pp. 339–403, 1997.
Paneli, D. and Gutfinger, C., Fluid Mechanics, Cambridge Univ. Press, Cambridge, 1997.
Parker, A., On the Camassa–Holm equation and a direct method of solution. I. Bilinear form and solitary waves, Proc. Roy. Soc. Lond. Ser. A, Vol. 460, pp. 2929–2957, 2004.
Parker, A., On the Camassa–Holm equation and a direct method of solution. II. Soliton solutions, Proc. R. Soc. Lond. Ser. A, Vol. 461, pp. 3611–3632, 2005.
Parker, A., On the Camassa–Holm equation and a direct method of solution. III. N-soliton solutions, Proc. Roy. Soc. Lond. Ser. A, Vol. 461, pp. 3893–3911, 2005.
Parker, A., A factorization procedure for solving the Camassa–Holm equation, Inverse Problems, Vol. 22, No. 2, pp. 599–609, 2006.
Parkes, E. J., Explicit solutions of the reduced Ostrovsky equation, Chaos, Solitons and Fractals, Vol. 31, pp. 602–610, 2007.
Parkes, E. J., Observations on the tanh-coth expansion method for finding solutions to nonlinear evolution equations, Appl. Math. Comp., Vol. 217, No. 4, pp. 1749–1754, 2010.
Parkes, E. J. and Duffy, B. R., An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations, Comput. Phys. Commun., Vol. 98, pp. 288–300, 1996.
Pascucci A., Kolmogorov equations in physics and in finance, In: Progress in Nonlinear Differential Equations and Their Applications, Birkhauser, Vol. 63, pp. 313–324, 2005.
Pascucci, A. and Polidoro, S., On the Cauchy problem for a non linear Kolmogorov equation, SIAM J. Math. Anal., Vol. 35, No. 3, pp. 579–595, 2003.
Pattle, R. E., Diffusion from an instantaneous point source with a concentration-dependent coefficient, J. Mech. Appl. Math., Vol. 12, pp. 407–409, 1959.
Paul, R. and Pillow, A. F., Conically similar viscous flows, Parts 2 and 3, Fluid Mech., Vol. 155, pp. 343–358 and 359–379, 1985.
Pavlov, M. V., The Calogero equation and Liouville-type equations, Theor. Math. Phys., Vol. 128, No. 1, pp. 927–932, 2001.
Pavlov, M. V., Integrability of hydrodynamic-type Egorov systems, Theor. Math. Phys., Vol. 150, No. 2, pp. 263–284, 2007.
Pavlovskii, Yu. N., Investigation of some invariant solutions to the boundary layer equations [in Russian], Zhurn. Vychisl. Mat. i Mat. Fiziki, Vol. 1, No. 2, pp. 280–294, 1961.
Pearson, C. E., Numerical solutions for the time-dependent viscous flow between two rotating coaxial disks, J. Fluid Mech., Vol. 21, pp. 623–633, 1965.
Pelyukh, G. P. and Sharkovskii, O. M., Introduction to the Theory of Functional Equations [in Russian], Naukova Dumka, Kiev, 1974.
Pen'kovskii, V. I., One-dimensional problem of the solution and leaching of salts at high values of the peclet number, J. Appl. Mech. Tech. Physics, Vol 10, No. 2, pp. 327–331, 1969.
Penney, W. G. and Price, A. T., Finite periodic stationary gravity waves in a perfect liquid, Part 2, Phil. Trans. R. Soc. Lond. A, Vol 224, pp. 254–284, 1952.
Peregrine, D. N., Calculations of the development of an undular bore, J. Fluid Mech., Vol. 25, p. 321, 1966.
Pernik, A. D., Cavitation Problems [in Russian], Sudostroenie, Leningrad, 1966.
Perring, J. K. and Skyrme, T. R., A model unified field equation, Nuclear Physics, Vol. 31, pp. 550–555, 1962.
Petrovskii, I. G., Lectures on the Theory of Ordinary Differential Equations [in Russian], Nauka, Moscow, 1970.
Philip, J. R., General method of exact solution of the concentration-dependent diffusion equation, Australian J. Physics, Vol. 13, No. 1, pp. 13–20, 1960.
Pike, R. and Sabatier, P. (Eds.), Scattering: Scattering and Inverse Scattering in Pure and Applied Science, Vols. 1 and 2, Academic Press, San Diego, 2002.
Pillow, A. F. and Paul, R., Conically similar viscous flows. Part 1. Basic conservation principles and characterization of axial causes in swirl-free flow, Fluid Mech., Vol. 155, pp. 327–341, 1985.
Plebanski, J. F., Some solutions of complex Einstein equations, J. Math. Phys., Vol. 16, pp. 2395–2402, 1975.
Plesset, M. S. and Prosperetti, A., Bubble dynamics and cavitation, Annual Rev. of Fluid Mech., Vol. 9, pp. 145–185, 1977.
Poincare, H., Sur les equations aux derives partielles de la physique mathematique, Amer. J. Math., Vol. 12, pp. 221–294, 1890.
Poiseuille, J. L. M., Recherches experimenteles sur le mouvement des liquides dans les tubes de tres petits diametres, Comptes Rendus Acad. Sci., Paris, Vol. 11, pp. 961–967, pp. 1041–1048, 1840 Vol. 12, pp. 112–115, 1841.
Pokhozhaev, S. I., On an L. V. Ovsiannikov's problem [in Russian], Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 5–10, 1989.
Polubarinova–Kochina, P. Ya., Theory of Groundwater Movement [in Russian], Nauka, Moscow, 1977 [see also English translation, Princeton Univ. Press, 1962].
Polyanin, A. D., On the integration of nonlinear unsteady convective heat/mass exchange equations [in Russian], Doklady AN USSR, Vol. 251, No. 4, pp. 817–820, 1980.
Polyanin, A. D., Method for solution of some non-linear boundary value problems of a non-stationary diffusion-controlled (thermal) boundary layer, Int. J. Heat Mass Transfer, Vol. 25, No. 4, pp. 471–485, 1982.
Polyanin, A. D., Partial separation of variables in unsteady problems of mechanics and mathematical physics, Doklady Physics, Vol. 45, No. 12, pp. 680–684, 2000.
Polyanin, A. D., Exact solutions and transformations of the equations of a stationary laminar boundary layer, Theor. Foundations of Chemical Engineering, Vol. 35, No. 4, pp. 319–328, 2001.
Polyanin, A. D., Transformations and exact solutions containing arbitrary functions for boundary-layer equations, Doklady Physics, Vol. 46, No. 7, pp. 526–531, 2001.
Polyanin, A. D., Exact solutions to the Navier–Stokes equations with generalized separation of variables, Doklady Physics, Vol. 46, No. 10, pp. 726–731, 2001.
Polyanin, A. D., Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman Hall/CRC Press, Boca Raton, 2002.
Polyanin, A. D., Nonclassical (noninvariant) traveling-wave solutions and self-similar solutions, Doklady Mathematics, Vol. 70, No. 2, pp. 790–793, 2004.
Polyanin, A. D., Exact solutions of nonlinear sets of equations of the theory of heat and mass transfer in reactive media and mathematical biology, Theor. Foundations of Chemical Engineering, Vol. 38, No. 6, pp. 622–635, 2004.
Polyanin, A. D., Systems of Partial Differential Equations [online], EqWorld – The World of Mathematical Equations, 2004 (see: http://eqworld.ipmnet.ru/en/solutions/syspde.htm).
Polyanin, A. D., Exact solutions of nonlinear systems of diffusion equations for reacting media and mathematical biology, Doklady Mathematics, Vol. 71, No. 1, pp. 148–154, 2005.
Polyanin, A. D., New classes of exact solutions to general nonlinear equations and systems of equations in mathematical physics, Doklady Mathematics, Vol. 421, No. 6, pp. 744–748, 2008.
Polyanin, A. D., On the nonlinear instability of the solutions of hydrodynamic-type systems, JETP Letters, Vol. 90, No. 3, pp. 217–221, 2009.
Polyanin, A. D., Exact solutions of the nonlinear instability of the solutions of the Navier–Stokes equations: Formulas for constructing exact solutions, Theor. Foundations of Chemical Engineering, Vol. 43, No. 6, pp. 881–888, 2009.
Polyanin, A. D., Von Mises- and Crocco-type transformations: order reduction of nonlinear equations, RF-pairs and Backlund transformations, Doklady Mathematics, Vol. 81, No. 1, pp. 160–165, 2010.
Polyanin, A. D. and Aristov, S. N., Systems of hydrodynamic type equations: exact solutions, transformations, and nonlinear stability, Doklady Physics, Vol. 54, No. 9, pp. 429–434, 2009.
Polyanin, A. D. and Dilman, V. V., Methods of Modeling Equations and Analogies in Chemical Engineering, CRC Press – Begell House, Boca Raton, 1994.
Polyanin, A. D., Kutepov, A. M., Vyazmin, A. V., and Kazenin, D. A., Hydrodynamics, Mass and Heat Transfer in Chemical Engineering, Taylor Francis, London, 2002.
Polyanin, A. D. and Manzhirov, A. V., Handbook of Mathematics for Engineers and Scientists, Chapman Hall/CRC Press, Boca Raton, 2007.
Polyanin A. D., Vyazmin A. V., Zhurov A. I., and Kazenin D. A., Handbook of Exact Solutions of Heat and Mass Transfer Equations [in Russian], Faktorial, Moscow, 1998.
Polyanin, A. D. and Vyazmina, E. A., New classes of exact solutions to general nonlinear heat (diffusion) equations, Doklady Mathematics, Vol. 72, No. 2, pp. 798–801, 2005.
Polyanin, A. D. and Vyazmina, E. A., New classes of exact solutions to nonlinear systems of reaction-diffusion equations, Doklady Mathematics, Vol. 74, No. 1, pp. 597–602, 2006.
Polyanin, A. D., Vyazmina, E. A., and Bedrikovetskii, P. G., New classes of exact solutions to nonlinear sets of equations in the theory of filtration and convective mass transfer, Theor. Foundations of Chemical Engineering, Vol. 41, No. 5, pp. 556–564, 2007.
Polyanin, A. D. and Zaitsev, V. F., Equations of an unsteady-state laminar boundary layer: general transformations and exact solutions, Theor. Foundations of Chemical Engineering, Vol. 35, No. 6, pp. 529–539, 2001.
Polyanin, A. D. and Zaitsev, V. F., Handbook of Nonlinear Mathematical Physics Equations [in Russian], Fizmatlit, Moscow, 2002.
Polyanin, A. D. and Zaitsev, V. F., Handbook of Exact Solutions for Ordinary Differential Equations, 2nd ed., Chapman Hall/CRC Press, Boca Raton, 2003.
Polyanin, A. D. and Zaitsev, V. F., Handbook of Nonlinear Partial Differential Equations, 1st ed., Chapman Hall/CRC Press, Boca Raton, 2004.
Polyanin, A. D., Zaitsev, V. F., and Moussiaux, A., Handbook of First Order Partial Differential Equations, Taylor Francis, London, 2002.
Polyanin, A. D., Zaitsev, V. F., and Zhurov, A. I., Methods for the Solution of Nonlinear Equations of Mathematical Physics and Mechanics [in Russian], Fizmatlit, Moscow, 2005.
Polyanin, A. D. and Zhurov, A. I., Exact solutions to nonlinear equations of mechanics and mathematical physics, Doklady Physics, Vol. 43, No. 6, pp. 381–385, 1998.
Polyanin, A. D. and Zhurov, A. I., The generalized and functional separation of variables in mathematical physics and mechanics, Doklady Mathematics, Vol. 65, No. 1, pp. 129–134, 2002.
Polyanin, A. D. and Zhurov, A. I., Methods of generalized and functional separation of variables in the hydrodynamic and heat- and mass- transfer equations, Theor. Foundations of Chemical Engineering, Vol. 36, No. 3, pp. 201–213, 2002.
Polyanin, A. D. and Zhurov, A. I., The von Mises transformation: order reduction and construction of Backlund transformations and new integrable equations [online], EqWorld – The World of Mathematical Equations, 2009 (see: http://eqworld.ipmnet.ru/en/methods/methods-pde/mises/mises-transformation.htm); see also arXiv:0907.0586v2 [math-ph].
Polyanin, A. D. and Zhurov, A. I., The Crocco transformation: order reduction and construction of Backlund transformations and new integrable equations [online], EqWorld – The World of Mathematical Equations, 2009 (see: http://eqworld.ipmnet.ru/en/methods/methods-pde/crocco-transformation.pdf); see also arXiv:0907.3170v1 [nlin.SI].
Polyanin, A. D., Zhurov, A. I., and Vyazmin, A. V., Generalized separation of variables in nonlinear heat and mass transfer equations, J. Non-Equilibrium Thermodynamics, Vol. 25, No. 3/4, pp. 251–267, 2000.
Polyanin, A. D., Zhurov, A. I., and Vyazmina, E. A., Exact solutions to nonlinear equations and systems of equations of general form in mathematical physics, AIP Conference Proceedings, Vol. 1067, pp. 64–86, 2008.
Pomeau, Y., Ramani, A., and Grammaticos, B., Structural stability of the Korteweg–de Vries solitons under a singular perturbation, Physica D, Vol. 31, No. 1, 127–134, 1988.
Pommaret, J. F., Systems in Partial Differential Equations and Lie Pseudogroups, Math. and its Appl., Vol. 14, New York, 1978.
Pontryagin, L. S., Boltyansky, V. G., Gamkrelidze, R. V., and Mishchenko, E. F., Mathematical Theory of Optimal Processes, Wiley-Interscience, New York, 1962.
Popovich, R. O. and Ivanova, N. M., New results on group classification of nonlinear diffusion.convection equations, J. Phys. A: Math. Gen., Vol. 37, pp. 7547–7565, 2004.
Popovich, R. O. and Ivanova, N. M., Potential equivalence transformations for nonlinear diffusion.convection equations, J. Phys. A: Math. Gen., Vol. 38, pp. 3145–3155, 2005.
Popovich, R. O., Vaneeva, O. O., and Ivanova, N. M., Potential nonclassical symmetries and solutions of fast diffusion equation, Phys. Letters A, Vol. 362, pp. 166–173, 2007.
Popovich, R. O., Vaneeva, O. O., More common errors in finding exact solutions of nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simul., Vol. 15, pp. 3887–3899, 2010.
Prager, S., Spiral flow in a stationary porous pipe, Phys. Fluids, Vol. 7, pp. 907–908, 1964.
Prager, V., Three-dimensional flow in homogeneous contract, Mekhanika [in Russian], Sbornik perevodov i obzorov inostr. lit., Vol. 3, p. 23, 1958.
Prosperetti, A., A generalization of the Rayleigh–Plesset equation of bubble dynamics, Phys. Fluids, Vol. 25, No. 3, pp. 409–410, 1982.
Proudman, J., Note on the motion of viscous liquids in channels, Philos. Mag., Vol. 28, pp. 30–36, 760, 1914.
Proudman, J. and Johnson, K., Boundary-layer growth near a rear stagnation point, J. Fluid Mech., Vol. 12, pp. 161–168, 1962.
Proudman, I. and Pearson, J. R. A., Expansions at small Reynolds number for the flow past a sphere and circular cylinder, J. Fluid Mech., Vol. 2, No. 3, pp. 237–262, 1957.
Pucci, E. and Saccomandi, G., Contact transformation and solution by reduction of partial differential equations, J. Phys. A: Math Gen., Vol. 27, pp. 177–184, 1994.
Pucci, E. and Saccomandi, G., Evolution equations, invariant surface conditions and functional separation of variables, Physica D, Vol. 139, pp. 28–47, 2000.
Pukhnachov, V. V., Group properties of the Navier–Stokes equations in the plane case, J. Appl. Math. Tech. Phys., No. 1, pp. 83–90, 1960.
Pukhnachov, V. V., A plane steady-state flow of a viscous incompressible fluid with rectilinear free boundaries, In: Numerical Methods in Continuum Mechanics [in Russian], Novosibirsk, Vol. 2, No. 4, pp. 67–75, 1971.
Pukhnachov, V. V., Invariant solutions of the Navier–Stokes equations describing flows with free boundaries, Doklady AN SSSR [in Russian], Vol. 202, No. 2, pp. 302–305, 1972.
Pukhnachov, V. V., Exact multidimensional solutions of the nonlinear diffusion equation, J. Appl. Mech. Tech. Phys., Vol. 36, No. 2, pp. 169–176, 1995.
Pukhnachov, V. V., Nonstationary viscous flows with a cylindrical free surface, In: Topics in Nonlinear Analysis. The Herbert Amann Anniversary Volume, Birkhauser, Basel, pp. 655–677, 1998.
Pukhnachov, V. V., On the problem of viscous strip deformation with a free boundary, Comptes Rendus Acad. Sci., Paris, Vol. 328, Ser. 1, pp. 357–362, 1999.
Pukhnachov, V. V., Symmetries in the Navier–Stokes Equations [in Russian], Uspekhi Mekhaniki, Vol. 4, No. 1, pp. 6–76, 2006.
Putkaradze, V. and Dimon, P., Nonuniform two-dimensional flow from a source, Phys. Fluids, Vol. 12, pp. 66–70, 2000.
Qin, M., Mei, F., and Fan, G., New explicit solutions of the Burgers equation, Nonlinear Dyn., Vol. 48, pp. 91–96, 2007.
Quispel, J. R. W., Nijhoff, F. W., and Capel, H. W., Linearization of the Boussinesq equation and the modified Boussinesq equation, Phys. Lett. A, Vol. 91, pp. 143–145, 1982.
Radayev, Yu. N., Limiting state of a neck of arbitrary shape in a rigid-plastic solid, Mechanics of Solids, Vol. 23, No. 6, pp. 62–68, 1988.
Rajappa, N. R., Nonsteady plane stagnation point flow with hard blowing, Z. Angew. Math. Mech. (ZAMM), Vol. 59, pp. 471–473, 1979.
Rao, A. R. and Kasiviswanathan, S. R., On exact solutions of the unsteady Navier–Stokes equations –- the vortex with instantaneous curvilinear axis, Int. J. Eng. Sci., Vol. 25, pp. 337–349, 1987.
Rassias, T. M., Functional Equations and Inequalities, Kluwer Academic, Dordrecht, 2000.
Rayleigh, Lord, On the motion of solid bodies through viscous liquids, Philos. Mag., Vol. 21, pp. 697–711, 1911.
Rayleigh, Lord, Deep water waves, progressive or stationary, to the third order of approximation, Phil. Trans. R. Soc. Lond. A, Vol. 91, pp. 345–353, 1915.
Remoissenet, M., Waves Called Solitons, 3rd ed., Springer-Verlag, Heidelberg, 1999.
Reyes, E. G., Geometric integrability of the Camassa–Holm equation, Lett. Math. Phys., Vol. 59, No. 2, pp. 117–131, 2002.
Rhee, H., Aris, R., and Amundson, N. R., On the theory of multicomponent chromatography, Phil. Trans. Royal Soc., Ser. A., Vol. 267, pp. 419–455, 1970.
Rhee, H., Aris, R., and Amundson, N. R., First Order Partial Differential Equations, Vol. I, Prentice Hall, Englewood Cliffs, 1986.
Rhee, H., Aris, R., and Amundson, N. R., First Order Partial Differential Equations, Vol. II, Prentice Hall, Englewood Cliffs, 1989.
Riabouchinsky, D., Quelques considerations sur les mouvements plans rotationnels dun liquide, Comptes Rendus Acad. Sci., Paris, Vol. 179, pp. 1133–1136, 1924.
Richards, D., Advanced Mathematical Methods with Maple, Cambridge University Press, Cambridge, 2002.
Riley, N. and Vasantha, R., An unsteady stagnation-point flow, Quart. J. Mech. Appl. Math., Vol. 42, pp. 511–521, 1988.
Robins, A. J. and Howarth, J. A., Boundary-layer development at a two-dimensional rear stagnation point, Fluid Mech., Vol. 56, pp. 161–171, 1972.
Robinson, A. R. and Welander, P., Thermal circulation on a rotating sphere with application to the oceanic thermocline, J. Marine Res., Vol. 21, No. 1, p. 25, 1963.
Rogers, M. H. and Lance, G. N., The rotationally symmetric flow of a viscous fluid in the presence of an infinite rotating disk, J. Fluid Mech., Vol. 7, pp. 617–631, 1960.
Rogers, C. and Ames, W. F., Nonlinear Boundary Value Problems in Science and Engineering, Academic Press, New York, 1989.
Rogers, C., and Ruggeri, T., A reciprocal Backlund transformation: application to a nonlinear hyperbolic model in heat conduction, Lett. Nuovo Cimento, Vol. 44, p. 289, 1985.
Rogers, C., and Shadwick W. F., Backlund Transformations and Their Applications, Academic Press, New York, 1982.
Romanovskii, Yu. M., Stepanova, N. V., and Chernavskii, D. S., Mathematical Biophysics [in Russian], Nauka, Moscow, 1984.
Rosen, G., Dilatation covariance and exact solutions in local relativistic field theories, Phys. Rev., Vol. 183, pp. 1186–1191, 1969.
Rosen, G., Method for the exact solution of a nonlinear diffusion, Phys. Rev. Letters, Vol. 49, No. 25, pp. 1844–1846, 1982.
Rosenau, P., Nonlinear dispersion and compact structures, Phys. Rev. Letters, Vol. 73, No. 13, pp. 1737–1741, 1994.
Rosenau, P., Compact and noncompact dispersive patterns, Phys. Letters A., Vol. 275, No. 3, pp. 193–203, 2000.
Rosenau, P. and Hyman, J. M., Compactons, solitons with finite wavelength, Phys. Rev. Letters, Vol. 70, No. 5, pp. 564–567, 1993.
Rosenau, P. and Levy, D., Compactons in a class of nonlinearly quintic equations, Phys. Letters A., Vol. 252, pp. 297–306, 1999.
Rosenhead, L., The steady two-dimensional radial flow of viscous fluid between two inclined plane walls, Proc. Roy. Soc. London, Ser. A, Vol. 175, pp. 436–467, 1940.
Ross, C. C., Differential Equations: An Introduction with Mathematica, Springer, New York, 1995.
Rott, N., Unsteady viscous flow in the vicinity of a stagnation point, Quart. Appl. Math., Vol. 13, No. 4, pp. 444–451, 1956.
Rott, N., On the viscous core of a line vortex, Z. Angew. Math. Phys., Vol. 9, pp. 543–553, 1958.
Rosenhead, L., Laminar Boundary Layers, Dover Publ., New York, 1988.
Rozendorn, E. R., Some classes of particular solutions to the equation z_xxz_yy−z_xy²+ a grad z=0 and their application to meteorological problems [in Russian], Vestnik Moskovskogo Universiteta, Ser. 1 (Mat. i Meh.), No. 2, pp. 56–58, 1984.
Rozhdestvenskii, B. L. and Yanenko, N. N., Systems of Quasilinear Equations and Their Applications to Gas Dynamics, American Mathematical Society, Providence, RI, 1983.
Rudenko, O. V. and Soluyan, S. I., Theoretical Foundations of Nonlinear Acoustics [in Russian], Nauka, Moscow, 1975.
Rudenko, O. V. and Robsman, V. A., Equation of nonlinear waves in scattering medium [in Russian], Doklady RAN, Vol. 384, No. 6, pp. 735–759, 2002.
Rudykh, G. A. and Semenov, E. I., On new exact solutions of a one-dimensional nonlinear diffusion equation with a source (sink) [in Russian], Zhurn. Vychisl. Matem. i Matem. Fiziki, Vol. 38, No. 6, pp. 971–977, 1998.
Rudykh, G. A. and Semenov, E. I., Non-self-similar solutions of a many-dimensional nonlinear diffusion equation [in Russian], Mat. Zametki, Vol. 67, No. 2, pp. 250–256, 2000.
Rumer, Yu. B., A problem on a submerged jet [in Russian], Appl. Math. and Mech. (PMM), Vol. 16, No. 2, pp. 255–256, 1952.
Ryzhov, O. S. and Khristianovich, S. A., On nonlinear reflection of weak shock waves, J. Appl. Math. Mech., Vol. 22, pp. 826–843, 1958.
Ryzhov, O. S. and Shefter, G. M., On unsteady gas flows in Laval nozzles, Soviet Physics Dokl., Vol. 4, pp. 939–942, 1958.
Sabitov, I. Kh., On solutions of the equation Δ u = f(x,y)e^cu in some special cases [in Russian], Mat. Sbornik, Vol. 192, No. 6, pp. 89–104, 2001.
Saccomandi, G., A remarkable class of non-classical symmetries of the steady two-dimensional boundary-layer equations, J. Physics A: Math. Gen., Vol. 37, pp. 7005–7017, 2004.
Safin, S. S. and Sharipov, R. A., Backlund autotransformation for the equation u_xt=e^u−e^−2u, Theor. Math. Phys., Vol. 95, No. 1, pp. 462–470, 1993.
Saied, E. A. and Abd El-Rahman, R. G., On the porous medium equation with modified Fourier's low: symmetries and integrability. Journal of the Physical Society of Japan, Vol. 68, No. 2, pp. 360–368, 1999.
Sakiadis, B. C., Boundary-layer behavior on continuous solid surfaces. 2. Boundary layer on a continuous flat surface, AIChE J., Vol. 7, No. 2, pp. 221–225, 1961.
Salas, A. H., Some solutions for a type of generalized Sawada–Kotera equation, Appl. Math. Comput., Vol. 196, No. 2, pp. 812–817, 2008\.
Salas, A. H., Exact solutions for the general fifth KdV equation by the exp function method, Appl. Math. Comput., Vol. 205, No. 1, pp. 291–297, 2008.
Salas, A. H. and Gomes, C. A., Computing exact solutions for some fifth KdV equations with forcing term, Appl. Math. Comput., Vol. 204, No. 1, pp. 257–260, 2008.
Samarskii, A. A., Galaktionov, V. A., Kurdyumov, S. P., and Mikhailov, A. P., Blow-up in Problems for Quasilinear Parabolic Equations, Walter de Gruyter, Berlin, 1995.
Samarskii, A. A. and Sobol', I. M., Examples of a numerical investigation of temperature waves, Zh. Vychisl. Mat. i Mat. Fiz., Vol. 3, No. 4, pp. 702–719, 1963.
Sattinger, D. H. and Weaver, O. L., Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics, Springer-Verlag, New York, 1986.
Saucez, P., Vande Wouwer, A., Schiesser, W. E., and Zegeling, P., Method of lines study of nonlinear dispersive waves, J. Comp. Appl. Math., 2003.
Sawada, K. and Kotera, T., A method for finding N-soliton solutions for the KdV equation and KdV-like equations, Prog. Theor. Phys., Vol. 51, pp. 1355–1367, 1974.
Schamel, H., A modified Korteweg–de Vries equation for ion acoustic waves due to resonant electrons, J. Plasma Phys., Vol. 9, pp. 377–387, 1973.
Schiesser, W. E., Computational Mathematics in Engineering and Applied Science: ODEs, DAEs, and PDEs, CRC Press, Boca Raton, 1994.
Schiesser, W. E. and Griffiths, G. W., A Compendium of Partial Differential Equation Models: Method of Lines Analysis with Matlab, Cambridge University Press, Cambridge, 2009.
Schlichting, H., Boundary Layer Theory, McGraw-Hill, New York, 1981.
Schofield, D. and Davey, A., Dual solutions of the boundary-layer equations at a point of attachment, J. Fluid Mech., Vol. 30, pp. 809–811, 1967.
Scott, A. C., The application of Backlund transforms to physical problems, In: Backlund Transformations (Ed. R. M. Miura), pp. 80–105, Springer-Verlag, Berlin, 1975.
Scott, A. C., Chu, F. Y., and McLaughlin D. W., The soliton: a new concept in applied science, Proc. IEEE, Vol. 61, pp. 1443–1483, 1973.
Sedov, L. I., Mechanics of Continuous Media, Vol. 1 [in Russian], Nauka, Moscow, 1973.
Sedov, L. I., Mechanics of Continuous Media, Vol. 2 [in Russian], Nauka, Moscow, 1984.
Sedov, L. I., Plane Problems of Hydrodynamics and Airdynamics [in Russian], Nauka, Moscow, 1980.
Sedov, L. I., Similarity and Dimensional Methods in Mechanics, CRC Press, Boca Raton, 1993.
Seeger, A., Donth, H., and Kochendorfer, A., Theorie der Versetzungen in eindimensionalen Atomreihen. III. Versetzungen, Eigenbewegungen und ihre Wechselwirkung, Z. Phys., Vol. 134, pp. 173–193, 1953.
Seeger, A. and Wesolowski, Z., Standing-wave solutions of the Enneper (sine-Gordon) equation, Int. J. Eng. Sci., Vol. 19, pp. 1535–1549, 1981.
Sekerzh-Zenkovich, Y. I., On the theory of standing waves of finite amplitude, Doklady Akad. Nauk. USSR, Vol. 58, pp. 551–554, 1947.
Serre, D., Systemes de Lois de Conservation, Tome I et II, Diderot, Paris, 1996.
Serrin, J., The swirling vortex, Philos. Trans. Roy. Soc. London, Ser. A, Vol. 271, pp. 325–360, 1972.
Sexl, T., Uber den von E. G. Richardson entdeckten `Annulareffekt,' Z. Phys., Vol. 61, pp. 349–362, 1930.
Shafranov, V. D., Plasma equilibrium in a magnetic field, Reviews of Plasma Physics, Vol. 2, p. 103, 1966.
Shan'ko, Yu. V., Some classes of plane steady-state flows of stratified fluids, Vichislitel'nye Tekhnologii [in Russian], Vol. 6, No. 5, pp. 106–117, 2001.
Shcheprov, A. V., An example of an outer flow of a viscous compressible fluid past a sphere for an arbitrary Reynolds number, Doklady AN, Vol. 395, No. 4, pp. 485–485, 2004.
Shercliff, J. A., Simple rotational flows, J. Fluid Mech., Vol. 82, No. 4, pp. 687–703, 1977.
Shigesada, N., Kawasaki, K., and Teramoto, E., Spatial segregation of interacting species, J. Theor. Biol., Vol. 79, pp. 83–99, 1979.
Shingareva, I. K., Investigation of Standing Surface Waves in a Fluid of Finite Depth by Computer Algebra Methods. PhD thesis [in Russian] Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 1995.
Shingareva, I. K. and Lizarraga-Celaya, C., High-order Asymptotic Solutions to Free Standing Water Waves by Computer Algebra, In: Proc. Maple Summer Workshop, pp. 1–28, University of Waterloo, Waterloo, Ontario, Canada, 2004.
Shingareva, I. K. and Lizarraga-Celaya, C., On frequency-amplitude dependences for surface and internal standing waves, J. Comp. Appl. Math., Vol. 200, pp. 459–470, 2007.
Shingareva, I. K. and Lizarraga-Celaya, C., Maple and Mathematica. A Problem Solving Approach for Mathematics, 2nd ed., Springer, Wien–New York, 2009.
Shingareva, I. K., Lizarraga-Celaya, C., and Ochoa Ruiz, A. D., Maple y Ondas Estacionarias. Problemas y Soluciones, Editorial Unison, Universidad de Sonora, Hermosillo, Mexico, 2006.
Shkadov, V. Ya., Solitary waves in a layer of viscous liquid, Fluid Dynamics, Vol. 12, No. 1, pp. 52–55, 1977.
Shmyglevskii, Yu. D., Analytical Investigation of Liquid and Gas Dynamics [in Russian], Editorial URSS, Moscow, 1999.
Shmyglevskii, Yu. D., and Shcheprov, A. V., Exact representation of certain axisymmetric vortex elements in a viscous incompressible fluid, Doklady Physics, Vol. 48, No. 12, pp. 685–687, 2003.
Shulman, Z. P. and Berkovskii, B. M., Boundary Layer in Non-Newtonian Fluids [in Russian], Nauka i Tehnika, Minsk, 1966.
Siddiqui, A. M., Kaloni, P. N., and Chandna, O. P., Hodograph transformation methods in non-Newtonian fluids, J. Eng. Math., Vol. 19, pp. 203–216, 1985.
Sidorov, A. F., Two classes of solutions of the fluid and gas mechanics equations and their connection to traveling wave theory, J. Appl. Mech. Tech. Phys., Vol. 30, No. 2, pp. 197–203, 1989.
Sidorov, A. F., Shapeev, V. P., and Yanenko, N. N., Method of Differential Constraints and its Applications in Gas Dynamics [in Russian], Nauka, Novosibirsk, 1984.
Sivashinsky, G. I., Instabilities, pattern formation and turbulence in flames, Annual Rev. of Fluid Mech., Vol. 15, pp. 179–199, 1983.
Skalak, F. M. and Wang, C. Y., Pulsatile flow in a tube with wall injection and suction, Appl. Sci. Res., Vol. 33, pp. 269–307, 1977.
Skalak, F. M. and Wang, C. Y., On the unsteady squeezing of a viscous fluid from a tube, J. Aust. Math. Soc. B, Vol. 21, pp. 65–74, 1979.
Skeel, R. D. and Berzins, M., A method for the spatial discretization of parabolic equations in one space variable, SIAM Journal on Scientific and Statistical Computing, Vol. 11, pp. 1–32, 1990.
Slezkin, N. A., On an exact solution of the equations of viscous flow [in Russian], Uchenye Zapiski Mosk. Gos. Univ., Rec. Moscow State Univ., Vol. 2, No. 11, pp. 89–90, 1934. See also Appl. Math. and Mech. (PMM), Vol. 18, p. 764, 1954.
Slezkin, N. A., Dynamics of Viscous Incompressible Fluid [in Russian], Gostekhizdat, Moscow, 1955.
Small, C. G., Functional Equations and How to Solve Them, Springer-Verlag, Berlin, 2007.
Smital, J. and Dravecky, J., On Functions and Functional Equations, Adam Hilger, Bristol-Philadelphia, 1988.
Smith, S. H., Eccentric rotating flows: exact unsteady solutions of the Navier–Stokes equations, Z. Angew. Math. Phys., Vol. 38, pp. 573–579, 1987.
Smoller, J., Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, New York, 1994.
Smyth, N. F. and Hill, J. M., High-order nonlinear diffusion, IMA J. Appl. Math., Vol. 40, pp. 73–86, 1988.
Sokolov, V. V. and Zhiber, A. V., On the Darboux integrable hyperbolic equations, Phys. Lett. A, Vol. 208, pp. 303–308, 1995.
Sokolovskii, V. V., Theory of Plasticity [in Russian], Vysshaja Shkola, Moscow, 1969.
Soliman, A. A., Exact solutions of the KdV-Burgers equation by Exp-function method, Chaos, Solitons and Fractals, Vol. 41, No. 2, pp. 1034–1039, 2009.
Sophocleous, C., Potential symmetries of nonlinear diffusion-convection equations, J. Phys. A: Math. Gen., Vol. 29, pp. 6951–6959, 1996.
Sophocleous, C., Potential symmetries of inhomogeneous nonlinear diffusion equations, Bull. Austral. Math. Soc., Vol. 61, pp. 507–521, 2000.
Sophocleous, C., Classification of potential symmetries of generalized inhomogeneous nonlinear diffusion equations, Physica A, Vol. 320, pp. 169–183, 2003.
Sparenberg, J. F., On the stream function in low Reynolds number flow for general curvilinear coordinates, In: Mathematical Approaches in Hydrodynamics (Ed. T. Miloh), SIAM, Philadelphia, pp. 461–472, 1991.
Squire, H. B., The round laminar jet, Quart. J. Mech. Appl. Math., Vol. 4, pp. 321–329, 1951.
Squire, H. B., Some viscous flow problems I. Jet emerging from a hole in a plane wall, Philos. Mag., Vol. 43, pp. 942–945, 1952.
Squire, H. B., Radial jets, 50 Jahre Grenzschichtforschung (Ed. H. Gortler and W. Tollmien), Vieweg, Braunschweig, pp. 47–54, 1955.
Starov, V. M., On the spreading of the droplets of non-volatile liquids over the solid surface, Colloid J. of the USSR, Vol. 45, No. 6, pp. 1009–1015, 1983.
Steeb, W.-H. and Euler, N., Nonlinear Evolution Equations and Painleve Test, World Scientific, Singapore, 1988.
Stein, C. F., Quantities which define conically self-similar free-vortex solutions to the Navier–Stokes equations uniquely, Fluid Mech., Vol. 438, pp. 159–181, 2001.
Stephani, H., Differential Equations: Their Solutions Using Symmetries, Cambridge Univ. Press, Cambridge, 1989.
Steuerwald, R., Uber ennepersche Flachen und Backlundsche Transformation, Abh. Bayer. Akad. Wiss. (Muench.), Vol. 40, pp. 1–105, 1936.
Stewartson, K., On the flow between two rotating coaxial disks, Proc. Cambridge Philos. Soc., Vol. 49, pp. 333–341, 1953.
Stokes, G. G., On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids, Trans. Cambridge Philos. Soc., Vol. 8, pp. 287–305, 1845.
Stokes, G. G., Report on recent researches in hydrodynamics, Rep. Br. Assoc., pp. 1–20, 1846. See also Math. Phys. Papers, Vol. 1, pp. 75–12, 1880.
Stokes, G. G., On the effect of the internal friction of fluid on the motion of pendulums, Trans. Cambridge Philos. Soc., Vol. 9, pp. 8–106, 1851.
Storm, M. L., Heat conduction in simple metals, J. Appl. Phys., Vol. 22, p. 940, 1951.
Strampp, W., Backlund transformations for diffusion equations, Physica D, No. 6, p. 113, 1982.
Strikwerda, L., Finite Difference Schemes and Partial Differential Equations, 2nd ed., SIAM, Philadelphia, 2004.
Stuart, J. T., On the effects of uniform suction on the steady flow due to a rotating disk, Quart. J. Mech. Appl. Math., Vol. 7, pp. 446–457, 1954.
Stuart, J. T., A solution of the Navier–Stokes and energy equations illustrating the response of skin friction and temperature of an infinite plate thermometer to fluctuations in the stream velocity, Proc. Roy. Soc. London, Ser. A, Vol. 231, pp. 116–130, 1955.
Stuart, J. T., Double boundary layers in oscillating viscous flows, J. Fluid Mech., Vol. 24, pp. 673–687, 1966.
Stuart, J. T., A simpler corner flow with suction, Q. J. Mech. Appl. Math., Vol. 19, pp. 217–220, 1966.
Stuart, J. T., The viscous flow near a stagnation point when the external flow has uniform vorticity, J. Aerosp. Sci., Vol. 26, pp. 124–125, 1959.
Subbotin, A. I., Minimax and Viscosity Solutions of Hamilton–Jacobi Equations [in Russian], Nauka, Moscow, 1991.
Subbotin, A. I., Generalized Solutions of First Order PDEs: the Dynamical Optimization Perspective, Birkhauser, Boston, 1995.
Sukhinin, S. V., Group properties and conservation laws of the transonic gas flow equation [in Russian], In: Dynamics of Continuous Media, No. 36, p. 130, 1978.
Sulem, C. and Sulem, P.-L., The Nonlinear Schrodinger Equation. Self-Focusing and Wave Collapse, Springer-Verlag, New York, 1999.
Sullivan, R. D., A two-cell vortex solution of the Navier–Stokes equations, J. Aerosp. Sci., Vol. 26, pp. 767–768, 1959.
Suslov, G. K., Theoretical Mechanics [in Russian], Gostekhizdat, Moscow, 1946.
Svinolupov, S. I., Second-order evolution equations possessing symmetries, Rus. Math. Surv., Vol. 40, pp. 263–264, 1985.
Svirshchevskii, S. R., Group Properties of the Hyperbolic System of Heat Transfer [in Russian], Preprint 20, Keldysh Institute of Applied Mathematics, Academy of Sciences, USSR, Moscow, 1986.
Svirshchevskii, S. R., Group Properties of the Heat Equation Accounting for the Heat-Flux Relaxation [in Russian], Preprint 105, Keldysh Institute of Applied Mathematics, Academy of Sciences, USSR, Moscow, 1988.
Svirshchevskii, S. R., Lie–Backlund symmetries of linear ODEs and generalized separation of variables in nonlinear equations, Phys. Lett. A, Vol. 199, pp. 344–348, 1995.
Svirshchevskii, S. R., Invariant linear subspaces and exact solutions of nonlinear evolutions equations, Nonlinear Math. Phys., Vol. 3, No. 1–2, pp. 164–169, 1996.
Szymanski, P., Quelques solutions exactes des equaions de l'hydrodynamique du fluide visqueux dans le cas dun tube cylindrique, J. Math. Pures Appl., Vol. 11, No. 9, pp. 67–107, 1932.
Tabor, M., Integrability in Nonlinear Dynamics: An Introduction, Wiley–Interscience Publ., New York, 1989.
Tadjbakhsh, I. and Keller, J. B., Standing surface waves of finite amplitude, J. Fluid Mech., Vol. 8, pp. 442–451, 1960.
Tam, K. K., A note on the asymptotic solution of the flow between two oppositely rotating infinite plane disks, SIAM J. Appl. Math., Vol. 17, pp. 1305–1310, 1969.
Tamada, K., Two-dimensional stagnation point flow impinging obliquely on a plane wall, J. Phys. Soc. Jap., Vol. 46, pp. 310–311, 1979.
Taras'ev, A. M., On an irregular differential game, Appl. Math. and Mech. (PMM), Vol. 49, No. 4, pp. 682–684, 1985.
Taylor, G. I., On the decay of vortices in a viscous fluid, Philos. Mag., Vol. 46, pp. 671–674, 1923.
Taylor, G. I., The formation of a blast wave by a very intense explosion. I. Theoretical discussion, Proc. Roy. Soc. A, Vol. 201, pp. 159–174, 1950.
Taylor, M. E., Partial Differential Equations III. Nonlinear Equations, Springer-Verlag, New York, 1996.
Temam, R., Navier–Stokes Equations, North-Holland Publ. Comp., Amsterdam–New York, 1979.
Terrill, R. M., An exact solution for flow in a porous pipe, Z. Angew. Math. Phys. (ZAMP), Vol. 33, pp. 547–552, 1982.
Terrill, R. M. and Cornish, J. P., Radial flow of a viscous, incompressible fluid between two stationary uniformly porous discs, Z. Angew. Math. Phys. (ZAMP), Vol. 24, pp. 676–688, 1973.
Terrill, R. M. and Shrestha, G. M., Laminar flow through parallel and uniformly porous walls of different permeability, Z. Angew. Math. Phys. (ZAMP), Vol. 16, pp. 470–482, 1965.
Terrill, R. M. and Thomas, P. W., On laminar flow through a uniformly porous pipe, Appl. Sci. Res., Vol. 21, pp. 37–67, 1969.
Terrill, R. M. and Thomas, P. W., Spiral flow in a porous pipe, Phys. Fluids, Vol. 16, pp. 356–359, 1973.
Thomas, J. W., Numerical Partial Differential Equations: Finite Difference Methods, Springer, New York, 1995.
Thorpe, J. F., Further investigation of squeezing flow between parallel plates, Dev. Theor. Appl. Mech., Vol. 3, pp. 635–648, 1967.
Tikhonov, A. N. and Samarskii, A. A., Equations of Mathematical Physics, Dover Publ., New York, 1990.
Timoshenko, S. and Woinowsky-Krieger, S., Theory of Plates and Shells, 2nd ed., McGraw-Hill, New York, 1959.
Ting, A. S., Cheb, H. H., and Lee, Y. C., Exact solutions of a nonlinear boundary value problem: the vortices of the two-dimensional sinh-Poisson equation, Physica D, pp. 37–66, 1987.
Titov, S. S., A method of finite-dimensional rings for solving nonlinear equations of mathematical physics [in Russian], In: Aerodynamics (Ed. T. P. Ivanova), Saratov Univ., Saratov, pp. 104–110, 1988.
Titov, S. S. and Ustinov, V. A., Investigation of polynomial solutions to the equations of motion of gases through porous media with integer isentropic exponent [in Russian], In: Approximate Methods of Solution of Boundary Value Problems in Solid Mechanics, AN USSR, Ural. Otd-nie Inst. Matematiki i Mekhaniki, pp. 64–70, 1985.
Toda, M., Studies of a nonlinear lattice, Phys. Rep., Vol. 8, pp. 1–125, 1975.
Tomotika, S. and Tamada, K., Studies on two-dimensional transonic flows of compressible fluid, Part 1, Quart. Appl. Math., Vol. 7, p. 381, 1950.
Topper, J. and Kawahara, T., Approximate equations for long nonlinear waves on a viscous fluid, J. Phys. Soc. Japan, Vol. 44, No. 2, pp. 663–666, 1978.
Trkal, V., A remark on the hydrodynamics of viscous fluids [in Czech], Cas. Pst. Mat, Fys., Vol. 48, pp. 302–311, 1919.
Tsarev, S. P., On Poisson brackets and one-dimensional Hamiltonian systems of hydrodynamic type, Soviet Math. Doklady, Vol. 31, No. 3, pp. 488–491, 1985.
Tsarev, S. P., Semi-Hamiltonian formalism for diagonal systems of hydrodynamic type and integrability of chromatography and electrophoresis equations, In: Modern Group Analysis: Lie–Backlund Groups and Quasilinear Systems, Preprint 106, LIIAN, pp. 30–35, 1989.
Tsarev, S. P., Geometry of Hamiltonian systems of hydrodynamic type. The generalised hodograph method, Mathematics in the USSR, Izvestiya, Vol. 377, No. 2, pp. 397–419, 1991.
Tsarev, S. P., On Darboux integrable nonlinear partial differential equations, Proc. Steklov Institute of Mathematics, Vol. 225, pp. 372–381, 1999.
Tsarev, S. P., Integrability of equations of hydrodynamic type: from the end of the 19th to the end of the 20th century, In: Integrability: the Seiberg–Witten and Whitham Equations (Eds. H. W. Braden and I. M. Krichever), Gordon Breach, Amsterdam, pp. 251–265, 2000.
Tsyfra, I., Non-local ansatze for nonlinear heat and wave equations, J. Phys. A: Math. Gen., Vol. 30, pp. 2251–2262, 1997.
Tsyfra, I., Messina, A., Napoli, A., and Tretynyk, V., On application of non-point and discrete symmetries for reduction of the evolution-type equations, In: Proc. of the Fifth Intern. Conf. Symmetry of Nonlinear Mathematical Physics, Proc. Inst. of Mathematics, Kyiv, Vol. 50, Pt. 1, pp. 271–276, 2004.
Tychynin, V. and Rasin, O., Nonlocal symmetries and generation of solutions for the inhomogeneous Burgers equation, In: Proc. of the Fifth Intern. Conf. Symmetry of Nonlinear Mathematical Physics, Proc. Inst. of Mathematics, Kyiv, Vol. 50, Pt. 1, pp. 277–281, 2004.
Tychynin, V., Petrova, O., and Tertyshnyk, O., Nonlocal symmetries and generation of solutions for partial differential equations, SIGMA, Vol. 3 (019), 12 pages, 2007.
Tzitzeica, G., Sur une nouvelle classe de surfaces, Comptes Rendus Acad. Sci., Paris, Vol. 150, pp. 955–956, 1910.
Uchida, S., The pulsating viscous flow superposed on the steady laminar motion of incompressible fluid in a circular pipe, Z. Angew. Math. Mech. (ZAMM), Vol. 7, pp. 403–421, 1956.
Uchida, S. and Aoki, H., Unsteady flows in a semi-infinite contracting or expanding pipe, J. Fluid Mech., Vol. 82, pp. 371–387, 1977.
Vakhnenko, V. O. and Parkes, E. J., Periodic and solitary-wave solutions of the Degasperis–Procesi equation, Chaos, Solitons and Fractals, Vol. 20, No. 5, pp. 1059–1073, 2004.
Van Dyke, M. D., Perturbation Methods in Fluid Mechanics, Parabolic Press, Stanford, CA, 1975.
Vekua, I. N., Remarks on the properties of solutions to equation Δ u = −Ke^2u [in Russian], Sib. Matem. Zhurn., Vol. 1, No. 3, pp. 331–342, 1960.
Vereshchagina, L. I., Group fibering of the spatial unsteady boundary layer equations [in Russian], Vestnik LGU, Vol. 13, No. 3, pp. 82–86, 1973.
Vinogradov, A. M., Local symmetries and conservation laws, Acta Appl. Math., Vol. 2, No. 7, pp. 21–78, 1984.
Vinogradov, A. M. and Krasil'shchik, I. S. (Eds.), Symmetries and Conservation Laws of Mathematical Physics Equations [in Russian], Faktorial, Moscow, 1997.
Vinogradov, A. M., Krasil'shchik, I. S., and Lychagin, V. V., Geometry of Jet Spaces and Nonlinear Partial Differential Equations, Gordon Breach, 1984.
Vinogradov, A. M., Krasil'shchik, I. S., and Lychagin, V. V., Introduction to Geometry of Nonlinear Differential Equations [in Russian], Nauka, Moscow, 1986.
Vinokurov, V. A. and Nurgalieva, I. G., Research of nonlinear equation of adiabatic motion of an ideal gas, p. 53, In: Nonclassical Equations of Mathematical Physics (Ed. V. N. Vragov), Novosibirsk, 1985.
Voinov, O. V., Dynamics of a viscous liquid wetting a solid via Van der Waals forces, J. Appl. Mechanics and Tech. Physics, Vol. 35, No. 6, pp. 875–890, 1994.
Volosov, K. A., A Method of Analysis for Evolution Systems with Distributed Parameters, DSc Thesis, Moscow, 2007.
Vorob'ev, E. M., Ignatovich N. V., and Semenova E. O., Invariant and partially invariant solutions of boundary value problems [in Russian], Doklady AN USSR, Vol. 306, No. 4, pp. 836–840, 1989.
Vvedensky, D. D., Partial Differential Equations with Mathematica, Addison-Wesley, Wokingham, 1993.
Vyazmina, E. A. and Polyanin, A. D., New classes of exact solutions to general nonlinear diffusion-kinetic equations, Theor. Foundations of Chemical Engineering, Vol. 40, No. 6, pp. 555–563, 2006.
Wachmann, C., A mathematical theory for the displacement of oil and water by alcohol, Soc. Petroleum Eng. J., Vol. 4, pp. 250–266, 1964.
Wadati, M., The exact solution of the modified Korteweg–de Vries equation, J. Phys. Soc. Japan, Vol. 32, pp. 1681–1687, 1972.
Wadati, M., The modified Korteweg–de Vries equation, J. Phys. Soc. Japan, Vol. 34, pp. 1289–1296, 1973.
Wadati, M. and Sawada, K., New representation of the soliton solution for the Korteweg–de Vries equation, J. Phys. Soc. Japan, Vol. 48, No. 1, pp. 312–318, 1980.
Wadati, M. and Sawada, K., Application of the trace method to the modified Korteweg–de Vries equation, J. Phys. Soc. Japan, Vol. 48, No. 1, pp. 319–326, 1980.
Wang, C. Y., On a class of exact solutions of the Navier–Stokes equations, J. Appl. Mech., Vol. 33, pp. 696–698, 1966.
Wang, C. Y., Pulsative flow in a porous channel, J. Appl. Mech., Vol. 38, pp. 553–555, 1971.
Wang, C. Y., Axisymmetric stagnation flow towards a moving plate, Am. Inst. Chem. Eng. J., Vol. 19, pp. 1080–1081, 1973.
Wang, C. Y., Axisymmetric stagnation flow on a cylinder, Q. Appl. Math., Vol. 32, pp. 207–213, 1974.
Wang, C. Y., The squeezing of a fluid between two plates, J. Appl. Mech., Vol. 43, pp. 579–582, 1976.
Wang, C. Y., The three-dimensional flow due to a stretching flat surface, Phys. Fluids, Vol. 27, pp. 1915–1917, 1984.
Wang, C. Y., Stagnation flow on the surface of a quiescent fluid – an exact solution of the Navier–Stokes equations, Quart. Appl. Math., Vol. 43, pp. 215–223, 1985.
Wang, C. Y., Exact solutions of the unsteady Navier–Stokes equations, Appl. Mech. Rev., Vol. 42, No. 11, pp. 269–282, 1989.
Wang, C. Y., Exact solutions for the Navier–Stokes equations – the generalized Beltrami flows, review and extension, Acta Mech., Vol. 81, pp. 69–74, 1990.
Wang, C. Y., Exact solutions for the steady-state Navier–Stokes equations, Annual Rev. of Fluid Mech., Vol. 23, pp. 159–177, 1991.
Wang, C. Y. and Watson, L. T., Squeezing of a viscous fluid between elliptic plates, Appl. Sci. Res., Vol. 35, pp. 195–207, 1979.
Wang, C. Y., Watson, L. T., and Alexander, K. A., Spinning of a liquid film from an accelerating disk, IMA J. Appl. Math., Vol. 46, pp. 201–210, 1991.
Warsi, Z. U. A., Fluid Dynamics, CRC Press, Boca Raton, 1993.
Waters, S. L., Solute uptake through the walls of a pulsating channel, J. Fluid Mech., Vol. 433, pp. 193–208, 2001.
Watson, J., A solution of the Navier–Stokes equations illustrating the response of a laminar boundary layer to a given change in the external stream velocity, Quart. J. Mech. Appl. Math., Vol. 11, pp. 302–325, 1958.
Watson, L. T. and Wang C. Y., Deceleration of a rotating disc in a viscous fluid, Phys. Fluids, Vol. 22, No. 12, pp. 2267–2269, 1979.
Watson, E., Boundary-layer growth, Proc. Roy. Soc. London, Ser. A, Vol. 231, pp. 104–116, 1955.
Wazwaz, A. M., General compactons solutions for the focusing branch of the nonlinear dispersive K(n, n) equations in higher dimensional spaces, Appl. Math. Comput., Vol. 133, No. 2/3, pp. 213–227, 2002.
Wazwaz, A. M., General solutions with solitary patterns for the defocusing branch of the nonlinear dispersive K(n, n) equations in higher dimensional spaces, Appl. Math. Comput., Vol. 133, No. 2/3, pp. 229–244, 2002.
Wazwaz, A. M., Peakons, kinks, compactons and solitary patterns solutions for a family of Camassa–Holm equations by using new hyperbolic schemes, Appl. Math. Comput., Vol. 182, No. 1, pp. 412–424, 2006.
Wazwaz, A. M., Kinks and solitons solutions for the generalized KdV equation with two power nonlinearities, Appl. Math. Comput., Vol. 183, No. 2, 1181–1189, 2006.
Wazwaz, A. M., New solitons and kink solutions for the Gardner equation, Commun. Nonlin. Science Numer. Simul., Vol. 12, No. 8, 1395–1404, 2007.
Wazwaz, A. M., The KdV equation, In: Handbook of Differential Equations, Evolutionary Equations, Vol. 4 (Eds. C. M. Dafermos and M. Pokorny), Elsevier, Amsterdam, 2008.
Wazwaz, A. M. and Mehanna, M. S., A variety of exact travelling wave solutions for the (2+1)-dimensional Boiti–Leon–Pempinelli equation, Appl. Math. Comp., Vol. 217, pp. 1484–1490, 2010.
Webb, G., Sorensen, M. P., Brio, M., Zakharian, A. R., and Moloney, J. V., Variational principles, Lie point symmetries, and similarity solutions of the vector Maxwell equations in non-linear optics, Phys. D., Vol. 191, pp. 49–80, 2004.
Weidman, P. D., New solutions for laminar boundary layers with cross flow, Z. Angew. Math. Phys., Vol. 48, No. 2, pp. 341–356, 1997.
Weidman, P. D. and Putkaradze, V., Axisymmetric stagnation flow obliquely impinging on a circular cylinder, Eur. J. Mech. B, Fluids, Vol. 22, pp. 123–131, 2003.
Weidman, P. D. and Putkaradze, V., Erratum: `Axisymmetric stagnation flow obliquely impinging on a circular cylinder,' Eur. J. Mech. B, Fluids, Vol. 24, pp. 788–790, 2005.
Weinbaum, S. and O'Brien, V., Exact Navier–Stokes solutions including swirl and cross flow, Phys. Fluids, Vol. 10, pp. 1438–1447, 1967.
Weinbaum, S., Lawrence, C. J., and Kuang, Y., The inertial draining of a thin fluid layer between parallel plates with a constant normal force. Part 1. Analytical solutions; inviscid and small but finite-Reynolds-number limits, J. Fluid Mech., Vol. 156, pp. 463–477, 1985.
Weiss, J., The Painleve property for partial differential equations. II: Backlund transformation, Lax pairs, and the Schwarzian derivative, J. Math. Phys., Vol. 24, No. 6, pp. 1405–1413, 1983.
Weiss, J., The sine-Gordon equations: complete and partial integrability, J. Math. Phys., Vol. 25, pp. 2226–2235, 1984.
Weiss, J., The Painleve property and Backlund transformations for the sequence of Boussinesq equations, J. Math. Phys., Vol. 26, pp. 258–269, 1985.
Weiss, J., Backlund transformations and the Painleve property, J. Math. Phys., Vol. 27, No. 5, pp. 1293–1305, 1986.
Weiss, J., Tabor, M., and Carnevalle, G., The Painleve property for partial differential equations, J. Math. Phys., Vol. 24, No. 3, pp. 522–526, 1983.
Wester, M. J., Computer Algebra Systems: A Practical Guide, Wiley, Chichester, 1999.
White, F. M., Laminar flow in a uniformly porous tube, J. Appl. Mech., Vol. 29, pp. 201–204, 1962.
Whitham, G. B., The Navier–Stokes equations of motion, In: Laminar Boundary Layers (Ed. L. Rosenhead), Clarendon Press, London, pp. 114–162, 1963.
Whitham, G. B., Non-linear dispersive waves, Proc. Roy. Soc. London, Ser. A, Vol. 283, pp. 238–261, 1965.
Whitham, G. B., Linear and Nonlinear Waves, Wiley, New York, 1974.
Wilson, G., On the quasi-Hamiltonian formalism of the KdV equation, Phys. Letters A, Vol. 132, pp. 445–450, 1988.
Wolfram, S., A New Kind of Science, Wolfram Media, Champaign, IL, 2002.
Wolfram, S., The Mathematica Book, 5th ed., Wolfram Media, Champaign, IL, 2003.
Womersley, J. R., Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known, J. Physiol., Vol. 127, pp. 553–563, 1955.
Womersley, J. R., Oscillatory motion of a viscous liquid in a thin-walled elastic tube: I. The linear approximation for long waves, Philos. Mag., Vol. 46, No. 7, pp. 199–221, 1955.
Yanenko, N. N., The compatibility theory and methods of integration of systems of nonlinear partial differential equations, In: Proceedings of All-Union Math. Congress, Vol. 2, pp. 613–621, Nauka, Leningrad, 1964.
Yang, K. T., Unsteady laminar boundary layers in a incompressible stagnation flow, J. Appl. Mech., Vol. 25, pp. 421–427, 1958.
Yao, Y., New type of exact solutions of nonlinear evolution equations via the new Sine-Poisson equation expansion method, Chaos, Solitons and Fractals, Vol. 26, pp. 1081–1086, 2005.
Yatseev, V. I., On one class of exact solutions to the equations of motion of a viscous fluid [in Russian], Zh. Eksp. Teor. Fiz., Vol. 20, No. 11, pp. 1031–1034, 1950.
Yih, C.-S., Stratified Flows, Academic Press, New York, 1980.
Yih, C.-S.,Wu, F., Garg, A. K., and Leibovich, S., Conical vortices: a class of exact solutions of the Navier–Stokes equations, Phys. Fluids, Vol. 25, pp. 2147–2158, 1982.
Yin, Z., On the Cauchy problem for an integrable equation with peakon solutions, Illinois J. Math., Vol. 47, No. 3, pp. 649–666, 2003.
Yin, Z., Global solutions to a new integrable equation with peakons, Indiana Univ. Math. J., Vol. 53, No. 4, pp. 1189–1209, 2004.
Yonga, X., Zhang, Z., and Chen, Y., Backlund transformation, nonlinear superposition formula and solutions of the Calogero equation. Phys. Let. A., Vol. 372, pp. 6273–6279, 2008.
Yu, S.-J., Toda, K., and Fukuyama, T., N-soliton solutions to a (2+1)-dimensional integrable equation, J. Phys. A., Vol. 31, pp. 10181–10186, 1998.
Yung, C. M., Verburg, K., and Baveye, P., Group classifications and symmetry reductions of the nonlinear diffusion-convection equation $u_t=(D(u)u_x)_x-K'(u)u_x$, Int. J. Non-Linear Mech., Vol. 29, pp. 273–278, 1994.
Zababakhin, E. I., Filling of bubbles in a viscous fluid, J. Appl. Mech. Tech. Phys., No. 6, p. 1129, 1960.
Zabusky, N. J., Exact solution for the vibrations of a nonlinear continuous model string, J. Math. Phys., Vol. 3, pp. 1028–1039, 1962.
Zaitsev, V. F. and Polyanin, A. D., Dynamics of spherical bubbles in non-Newtonian liquids, Theor. Found. Chem. Eng., Vol. 26, No. 2, pp. 185–190, 1992.
Zaitsev, V. F. and Polyanin, A. D., Handbook on Nonlinear Differential Equations: Applications in Mechanics, Exact Solutions [in Russian], Fizmatlit\,/\,Nauka, Moscow, 1993.
Zaitsev, V. F. and Polyanin, A. D., Discrete-Group Methods for Integrating Equations of Nonlinear Mechanics, CRC Press, Boca Raton, 1994.
Zaitsev, V. F. and Polyanin, A. D., Handbook of Partial Differential Equations: Exact Solutions [in Russian], Mezhdunarodnaya Programma Obrazovaniya, Moscow, 1996.
Zaitsev, V. F. and Polyanin, A. D., Exact solutions and transformations of nonlinear heat and wave equations, Doklady Mathematics, Vol. 64, No. 3, pp. 416–420, 2001.
Zaitsev, V. F. and Polyanin, A. D., Handbook of First-Order PDEs [in Russian], Fizmatlit, Moscow, 2003.
Zakharov, V. E., On the stochastization of one-dimensional chains of nonlinear oscillators [in Russian], Zhurn. Eksper. i Teor. Fiziki, Vol. 65, pp. 219–225, 1973.
Zakharov, V. E. and Faddeev, L. D., The Korteweg–de Vries equation: a completely integrable Hamiltonian system, Funct. Anal. Appl., Vol. 5, pp. 280–287, 1971.
Zakharov, V. E. and Shabat, A. B., Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Soviet Physics JETP, Vol. 34, pp. 62–69, 1972.
Zakharov, V. E. and Shabat, A. B., A scheme for the integration of nonlinear evolutionary equations of mathematical physics by the inverse scattering method [in Russian], Funkts. Analiz i ego Prilozh., Vol. 8, No. 3, pp. 43–53, 1974.
Zakharov, V. E., Takhtajan, L. A., and Faddeev, L. D., Complete description of solutions of the sin-Gordon equation [in Russian], Doklady AN USSR, Vol. 219, No. 6, pp. 1334–1337, 1973.
Zandbergen, P. J., New solutions of the Karman problem for rotating flows, Lecture Notes in Mathematics, Springer-Verlag, Berlin, Vol. 771, pp. 563–581, 1980.
Zandbergen, P. J. and Dijkstra, D., Non-unique solutions of the Navier–Stokes equations for the Karman swirling flow, J. Eng. Math., Vol. 11, pp. 167–188, 1977.
Zandbergen, P. J. and Dijkstra, D., Von Karman swirling flow, Annual Rev. of Fluid Mech., Vol. 19, pp. 465–491, 1987.
Zauderer, E., Partial Differential Equations of Applied Mathematics, John Wiley Sons, New York, 1983.
Zayko, Y. N. and Nefedov, I. S., New class of solutions of the Korteweg–de Vries–Burgers equation, Appl. Math. Lett., Vol. 14, pp. 115–121, 2001.
Zel'dovitch, B. Ya., Pilipetzky, N. F., and Shkunov, V. V., Wave Front Reversal [in Russian], Nauka, Moscow, 1985 [English translation: Principles of Phase Conjugation, Springer-Verlag, New York, 1985].
Zel'dovich, Ya. B. and Kompaneets, A. S., On the theory of propagation of heat with the heat conductivity depending upon the temperature, pp. 61–71, In: Collection in Honor of the Seventieth Birthday of Academician A. F. Ioffe [in Russian], Izdat. Akad. Nauk USSR, Moscow, 1950.
Zel'dovich, Ya. B. and Raiser, Yu. P., Physics of Shock Waves and High Temperature Hydrodynamics Phenomena, Vols. 1 and 2, Academic Press, New York, 1966 and 1967.
Zel'dovich, Ya. B. and Raizer, Yu. P., Elements of Gas Dynamics and the Classical Theory of Shock Waves, Academic Press, New York, 1968.
Zel'dovich, Ya. B., Barenblatt, G. I., Librovich, V. B., and Makhviladze, G. M., The Mathematical Theory of Combustion and Explosion, Consultants Bureau, Division of Plenum Press, New York, 1985.
Zhang, L., The extended tanh method and the exp-function method to solve a kind of nonlinear heat equation, Math. Prob. Engng., Vol. 2010, 2010. doi:10.1155/2010/935873.
Zhang, L., Explicit traveling wave solutions of five kinds of nonlinear evolution equations, J. Math. Anal. Appl., Vol. 379, pp. 91–124, 2011.
Zhdanov, R. Z., Separation of variables in the non-linear wave equation, J. Phys. A, Vol. 27, pp. L291–L297, 1994.
Zhdanov, R. Z., On relation between potential and contact symmetries of evolution equations, J. Math. Phys., 2009, Vol. 50, 053522 (DOI:10.1063/1.3138147).
Zhdanov, R. Z., Nonlocal symmetries of evolution equations, Nonlinear Dyn., 2010 (DOI:10.1007–s11071-009-9604-y).
Zhdanov, R. Z. and Lahno, V. I., Conditional symmetry of a porous medium equation, Physica D, Vol. 122, pp. 178–186, 1998.
Zhiber, A. V. and Sokolov, V. V., Exact integrable Liouville type hyperbolic equations [in Russian], Uspekhi Mat. Nauk, Vol. 56, No. 1, pp. 64–104, 2001.
Zhiber, A. V., Sokolov, V. V., and Startsev, S. Ya., On Darboux-integrable nonlinear hyperbolic equations [in Russian], Doklady RAN, Vol. 343, No. 6, pp. 746–748, 1995.
Zhu, G. C. and Chen, H. H., Symmetries and integrability of the cylindrical Korteweg–de Vries equation, J. Math. Phys., Vol. 27, No. 1, pp. 100–103, 1986.
Zhukov, M. Yu. and Yudovich, V. I., Mathematical theory of isotachophoresis, Doklady AN SSSR, Vol. 267, No. 2, pp. 334–338, 1982.
Zhuravlev, V. M., Exact solutions of the nonlinear diffusion equation u_t = Δ ln u+λu in a two-dimensional coordinate space, Theor. Math. Phys., Vol. 124, No. 2, pp. 1082–1093, 2000.
Zimmerman, R. L. and Olness, F., Mathematica for Physicists, Addison-Wesley, Reading, MA, 1995.
Zmitrenko, N. V., Kurdyumov, S. P., and Mikhailov, A. P., Theory of blow-up regimes in compressible media [in Russian], In: Contemporary Problems of Mathematics, Vol. 28 (Itogi Nauki i Tekhniki, VINITI AN USSR), Moscow, pp. 3–94, 1987.
Zmitrenko, N. V., Kurdyumov, S. P., Mikhailov, A. P., and Samarskii A. A., Appearance of Structures in Nonlinear Media and Transient Thermodynamics of Blow-up Regimes [in Russian], Preprint No. 74, Keldysh Institute of Applied Mathematics, Academy of Sciences, USSR, Moscow, 1976.
Zwillinger, D., Handbook of Differential Equations, Academic Press, San Diego, 1989 and 1998.

The EqWorld website presents extensive information on solutions to various classes of ordinary differential equations, partial differential equations, integral equations, functional equations, and other mathematical equations.

A. D. Polyanin and V. F. Zaitsev

Handbook of Nonlinear Partial Differential EquationsSecond Edition, Updated, Revised and Extended

Summary Preface Features Contents References Index (pdf 117K)

References

Handbook of Nonlinear Partial Differential Equations
Second Edition, Updated, Revised and Extended