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Books on Nonlinear Partial Differential Equations (Equations of Mathematical Physics)

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 Clarkson, P. A., Solitons, Non-linear Evolution Equations and Inverse Scattering, Cambridge Univ. Press, Cambridge, 1991.
Ablowitz, M. J. and Clarkson, P. A. (Editors), Solitons and Symmetries, Special issue of Journal of Engineering Mathematics, Kluwer, Dordrecht, Vol. 36, Issue 1/2, pp. 1–91, 1999.
Akhmediev, N. N. and Ankiewicz, A., Solitons. Nonlinear Pulses and Beams, Chapman & Hall, London, 1997.
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.
Anderson, R. L. and Ibragimov, N. H., Lie–Bäcklund Transformations in Applications, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1979.
Andreev, V. K., Kaptsov, O. V., Pukhnachov, V. V., and Rodionov, A. A., Applications of Group-Theoretical Methods in Hydrodynamics, Kluwer, Dordrecht, 1998.
Barenblatt, G. I., Dimensional Analysis, Gordon & Breach, New York, 1989.
Barenblatt, G. I., Scaling, Cambridge Univ. Press, Cambridge, 2003.
Baumann, G., Symmetry Analysis of Differential Equations with Mathematica, Springer-Verlag, New York, 2000.
Bluman, G.W. and Anco, S.C., Symmetry and Integration Methods for Differential Equations, Second Edition, Springer-Verlag, New York, 2002.
Bluman, G. W. and Cole, J. D., Similarity Methods for Differential Equations, Springer-Verlag, New York, 1974.
Bluman, G. W. and Kumei, S., Symmetries and Differential Equations, Springer-Verlag, New York, 1989.
Bullough, R. K. and Caudrey, P. J. (Editors), Solitons, Springer-Verlag, Berlin, 1980.
Calogero, F. and Degasperis, A., Spectral Transform and Solitons: Tolls to Solve and Investigate Nonlinear Evolution Equations, North-Holland Publishing Company, Amsterdam, 1982.
Cantwell, B. J., Introduction to Symmetry Analysis, Cambridge Univ. Press, Cambridge, 2002.
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.
Chowdhury, A. R., Painlevé Analysis and Its Applications, Chapman & Hall/CRC Press, Boca Raton, 2000.
Conte, R. (Editor), The Painlevé Property. One Century Later, Springer-Verlag, New York, 1999.
Conte, R. and Boccara, N. (Editors), Partially Integrable Evolution Equations in Physics, Kluwer, Dordrecht, 1990.
Courant, R. and Friedrichs, R., Supersonic Flow and Shock Waves, Springer-Verlag, New York, 1985.
Courant, R. and Hilbert, D., Methods of Mathematical Physics, Vols. 1 and 2, Wiley–Interscience Publ., New York, 1989.
Crank, J., The Mathematics of Diffusion, Clarendon Press, Oxford, 1975.
Dafermos, C. M., Hyperbolic Conservation Laws in Continuum Physics, Springer-Verlag, Berlin, 2000.
Danilov, V. G., Maslov V. P., and Volosov, K. A., Mathematical Modelling of Heat and Mass Transfer Processes, Kluwer, Dordrecht, 1995.
Dickey, L. A., Soliton Equations and Hamilton Systems, World Scientific, Singapore, 1991.
Dodd, R. K., Eilbeck, J. C., Gibbon, J. D., and Morris, H. C., Solitons and Nonlinear Wave Equations, Academic Press, London, 1982.
Drazin, P. G. and Johnson, R. S., Solitons: An Introduction, Cambridge Univ. Press, Cambridge, 1989.
Dresner, L., Similarity Solutions of Nonlinear Partial Differential Equations, Pitman, Boston, 1983.
Enns, R. H. and McGuire, G. C., Nonlinear Physics with Maple for Scientists and Engineers, 2nd ed., Birkhauser, Boston, 2000.
Faddeev, L. D. and Takhtajan, L. A., Hamiltonian Methods in the Theory of Solitons, Springer-Verlag, Berlin, 1987.
Filenberger, G., Solitons. Mathematical Method for Physicists, Springer-Verlag, Berlin, 1981.
Fushchich, W. I., Shtelen, W. M., and Serov, N. I., Symmetry Analysis and Exact Solutions of the Equations of Mathematical Physics, Kluwer, Dordrecht, 1993.
Gaeta, G., Nonlinear Symmetries and Nonlinear Equations, Kluwer, Dordrecht, 1994.
Galaktionov, V. A., Geometric Sturmian Theory of Nonlinear Parabolic Equations with Applications, Chapman & Hall/CRC Press, Boca Raton, 2004.
Galaktionov, V. A., Svirshchevskii, S. R., Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics, Chapman & Hall/CRC Press, Boca Raton, 2006.
Ganzha V.G. and Vorozhtsov E.V., Computer-Aided Analysis of Difference Schemes for Partial Differential Equations, Wiley-Interscience, New York, 1996.
Ganzha V.G. and Vorozhtsov E.V., Numerical Solutions for Partial Differential Equations: Problem Solving Using Mathematica, CRC Press, Boca Raton, 1996.
Godlewski, E. and Raviart, P.-A., Numerical Approximations of Hyperbolic Systems of Conservation Laws, Springer-Verlag, New York, 1996.
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.
Hydon, P. E., Symmetry Methods for Differential Equations: A Beginner's Guide, Cambridge Univ. Press, Cambridge, 2000.
Ibragimov, N. H., Transformation Groups Applied in Mathematical Physics, D. Reidel Publ., Dordrecht, 1985.
Ibragimov, N. H. (Editor), 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. (Editor), CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 2, Applications in Engineering and Physical Sciences, CRC Press, Boca Raton, 1995.
Ibragimov, N. H. (Editor), CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 3, CRC Press, Boca Raton, 1996.
Jeffrey, A., Quasilinear Hyperbolic Systems and Shock Waves, Pitman, London, 1976.
John, F., Partial Differential Equations, Springer-Verlag, New York, 1982.
Kevorkian, J., and Cole, J. D., Perturbation Methods in Applied Mathematics, Springer-Verlag, New York, 1981.
Klimov, D. M. and Zhuravlev, V. Ph., Group-Theoretic Methods in Mechanics and Applied Mathematics, Chapman & Hall/CRC Press, Boca Raton, 2002.
Korepin, V. E., Bogoliubov, N. N., and Izergin A. G., Quantum Inverse Scattering Method and Correlation Functions, Cambridge Univ. Press, Cambridge, 1997.
Krasil'shchik, I. S. and Vinogradov, A. M. (Editors), Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, American Mathematical Society, Providence, RI, 1999.
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.
Kuranishi, M., Lectures on Involutive Systems on Partial Differential Equations, Publ. Soc. Math., Saõ Paulo, 1967.
Lamb, G. L., Elements of Soliton Theory, Wiley, New York, 1980.
Lax, P., Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, Society of Industrial and Applied Math., Philadelphia, 1973.
LeVeque, R. J., Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002.
Logan, D. J., Nonlinear Partial Differential Equations, John Wiley & Sons Inc., New York, 1994.
Lonngren, K. and Scott, A. (Editors), Solitons in Action, Academic Press, New York, 1978.
Meirmanov, A. M., Pukhnachov, V. V., and Shmarev, S. I., Evolution Equations and Lagrangian Coordinates, Walter de Gruyter, Berlin, 1997.
Miura, R. M. (Editor), Bäcklund Transformations, Springer-Verlag, Berlin, 1976.
Miwa, T., Jimbo, M., and Date, E., Solitons. Differential Equations, Symmetries and Infinite-Dimensional Algebras, Cambridge Univ. Press, Cambridge, 2000.
Nayfeh, A. H., Perturbation Methods, John Wiley & Sons, New York, 1973.
Newell, A. C., Solitons in Mathematics and Physics, Soc. Indus. Appl. Math. (SIAM), Arizona, 1985.
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.
Olver, P. J., Application of Lie Groups to Differential Equations, Second Edition, Springer-Verlag, New York, 1993.
Olver, P. J., Equivalence, Invariants, and Symmetry, Cambridge Univ. Press, Cambridge, 1995.
Olver, P. J., Classical Invariant Theory, Cambridge Univ. Press, Cambridge, 1999.
Ovsiannikov, L. V., Group Analysis of Differential Equations, Academic Press, New York, 1982.
Pike, R. and Sabatier, P. (Editors), Scattering: Scattering and Inverse Scattering in Pure and Applied Science, Vols. 1 and 2, Academic Press, San Diego, 2002.
Polyanin, A. D., Handbook of Linear Partial Differential Equations for Engineers and Scientists (Supplement B), Chapman & Hall/CRC Press, Boca Raton, 2002.
Polyanin, A. D. and Manzhirov, A. V., Handbook of Mathematics for Engineers and Scientists (Chapters 15, T9, and T10), Chapman & Hall/CRC Press, Boca Raton, 2006.
Polyanin, A. D. and Zaitsev, V. F., Handbook of Nonlinear Partial Differential Equations, 2nd Edition, Chapman & Hall/CRC Press, Boca Raton, 2012.
Reidel, D. and Ball, J. S. (Editors), Systems of Non-Linear Partial Differential Equations, Kluwer, Dordrecht, 1983.
Rogers, C. and Ames, W. F., Nonlinear Boundary Value Problems in Science and Engineering, Academic Press, New York, 1989.
Rogers, C., and Shadwick W. F., Bäcklund Transformations and Their Applications, Academic Press, New York, 1982.
Rozhdestvenskii, B. L. and Yanenko, N. N., Systems of Quasilinear Equations and Their Applications to Gas Dynamics, Amer. Math. Society, Providence, 1983.
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.
Sachdev, P.L., Self-Similarity and Beyond: Exact Solutions of Nonlinear Problems, Chapman & Hall/CRC, Boca Raton, 2000.
Sattinger, D. H. and Weaver, O. L., Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics, Springer-Verlag, New York, 1986.
Serre, D., Systémes de Lois de Conservation, Tome I et II, Diderot, Paris, 1996.
Smoller J., Shock Waves and Diffusion-Reaction Equations, Springer-Verlag, New York, 1983.
Steeb, W.-H. and Euler, N., Nonlinear Evolution Equations and Painlevé Test, World Scientific, Singapore, 1988.
Stephani, H., Differential Equations: Their Solutions Using Symmetries, Cambridge Univ. Press, Cambridge, 1989.
Sulem, C. and Sulem, P.-L., The Nonlinear Schrödinger Equation. Self-Focusing and Wave Collapse, Springer-Verlag, New York, 1999.
Tabor, M., Chaos and Integrability in Nonlinear Dynamics: An Introduction, Wiley–Interscience Publ., New York, 1989.
Vinogradov, A. M., Krasil'shchik, I. S., and Lychagin, V. V., Geometry of Jet Spaces and Nonlinear Partial Differential Equations, Gordon & Breach, 1984.
Volpert, A. I., Volpert, Vit. A., and Volpert, Vl. A., Traveling Wave Solutions of Parabolic Systems, American Mathematical Society, Providence, RI, 1994.
Whitham, G. B., Linear and Nonlinear Waves, Wiley, New York, 1974.
Wouwer, A. V., Saucez, Ph., and Schiesser, W. E., Adaptive Method of Lines, Chapman & Hall/CRC Press, Boca Raton, 2001.
Zakharov, V. E. (Editor), What is Integrability?, Springer-Verlag, 1990.
Zwillinger, D., Handbook of Differential Equations, 3rd ed., Academic Press, Boston, 1997.

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