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Interesting Articles and Materials
Nonlinear Ordinary Differential Equations
- Calogero, F. and Payandeh, F., Explicitly
solvable systems of first-order ordinary differential equations with polynomial
right-hand sides, and their periodic variants, arXiv:submit/3789788 [math.DS], 11 Jun
- Dorodnitsyn, V.,
On the linearization of second-order differential
and difference equations, Symmetry, Integrability and Geometry: Methods and Applications,
Vol. 2, 2006.
- Estevez, P. G., Kuru, S., Negro, J., and Nieto, L. M.,
Factorization of a class of almost linear
second order differential equations, J. Phys. A: Math. Theor.,
Vol. 40, pp. 9819–9824, 2007.
- Goodall, R. and Leach, P. G. L.,
Generalized symmetries and the
Ermakov–Lewis invariant, J. Nonlinear Math. Phys.,
Vol. 12, No. 1, pp. 15–26, 2005.
- Kudryashov, N. A.,
Nonlinear differential equations
with exact solutions expressed via the Weierstrass function,
Zeitschrift fur Naturforschung, 2004.
- Yee, T. L. and Conte, R.,
Another integrable case in the Lorenz model
J. Phys. A: Math. Gen., Vol. 37, No. 10, 2004.
Nonlinear Partial Differential Equations
- Barannyk, T.,
Symmetry and exact solutions for systems of nonlinear
reaction-diffusion equations, Proc. Inst. Math. NAS of Ukraine, Vol. 43,
Pt. 1, pp. 80–85, 2002.
- Cherniha, R. M.,
New ansätze and exact solutions for nonlinear
reaction-diffusion equations arising in mathematical biology,
Symmetry in Nonlinear Math. Phys., Vol. 1, pp. 138–146, 1997.
- Clarkson, P. A. and Mansfield, E. L.,
Symmetry reductions and exact solutions of a
class of nonlinear heat equations, 2002.
- Dorodnitsyn, V. and Kozlov, R.,
A heat transfer with source: the complete set of invariant difference
schemes, J. Nonlinear Math. Physics,
Vol. 10, No. 1, 2003.
- Hamdi, S., Enright, W. H., Schiesser, W. E., and Gottlieb, J. J.,
Exact solutions of the generalized equal width wave equation, 2004.
- Ivanova, N. M.,
Exact solutions of diffusion-convection equations,
arXiv:0710.4000v1 [math-ph], 22 Oct 2007.
- Kalnins, E. G., Kress, J. M., Pogosyan, G., and Miller, W. (Jr.),
Comlete sets of invariants for dynamical systems that admit a separation of variables, 2002
- Kaptsov, O. V. and Verevkin, I. V.,
Differential constraints and exact solutions of nonlinear diffusion equations,
J. Phys. A: Math. Gen., Vol. 36, pp. 1401–1414, 2003.
- Kosovtsov, Yu. V.,
The general solutions of some nonlinear second order PDEs. I. Two independent variables, constant parameters,
arXiv:0801.4081v1 [math-ph], 2008.
- Kudryashov, N. A., and Loguinova, N. B.,
Be careful with the Exp-function method,
Communications in Nonlinear Science and Numerical Simulation, Vol. 14, Issue 5, pp. 1881–1890, 2009.
- Lahno, V., Zhdanov, R., and Magda, O.,
Group classification of nonlinear wave equations,
arXiv:nlin.SI/0405069 v1, 31 May 2004.
- Lapinska-Chrzczonowicz, M.,
Exact difference schemes for multidimensional heat conduction equations,
Comp. Methods Appl. Math., Vol. 7,
No. 2, pp. 178–190, 2007.
- Nikitin, A. G. and Wiltshire, R. J.,
Symmetries of systems of nonlinear
reaction-diffusion equations, Proc. Inst. Math. NAS of Ukraine, Vol. 30,
Pt. 1, pp. 47–59, 2000.
- Nikitin, A. G.,
Group classification of systems of non-linear
reaction-diffusion equations with general diffusion matrix. II. Diagonal diffusion matrix,
arXiv:math-ph/0411028 v1, 7 Nov 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, Theoretical Foundations of Chemical Engineering,
Vol. 38, No. 6, pp. 622–635, 2004.
- Polyanin, A. D. and Zhurov, A. I., Exact solutions of heat and
mass transfer equations, Matematica Contemporanea, Vol. 19, pp. 105–127, 2000.
- Polyanin, A. D. and Zhurov, A. I., Exact solutions to
nonlinear equations and systems of equations of general form in mathematical physics,
St-Petersburg, 14 April 2008.
- Polyanin, A. D. and Zhurov, A. I.,
The von Mises transformation:
order reduction and construction of Bäcklund transformations and new integrable equations,
EqWorld—The World of Mathematical Equations, 3 July 2009.
- Polyanin, A. D. and Zhurov, A. I.,
The Crocco transformation: order reduction and construction of Bäcklund transformations
and new integrable equations, arXiv:0907.3170v1 [nlin.SI], 21 July 2009.
- Popovych, R. O., and Ivanova, N. M,
New results of group classifications of nonlinear diffusion-convection equations,
arXiv:math-ph/0306035v1, 12 Jun 2003.
- Shingareva, I. and Lizárraga Celaya, C., Maple and standing waves, 2006.
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