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TitleSymbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs
Author(s) D. Baldwin, Ü. Göktaş, W. Hereman, L. Hong, R.S. Martino, J. Lyn Miller
TypeArticle in Journal
AbstractAlgorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and PDEs in terms of Jacobiís elliptic functions. For systems with parameters, the algorithms determine the conditions on the parameters so that the differential equations admit polynomial solutions in tanh, sech, combinations thereof, Jacobiís sn or cn functions. Examples illustrate key steps of the algorithms. The new algorithms are implemented in Mathematica. The package PDESpecialSolutions.m can be used to automatically compute new special solutions of nonlinear PDEs. Use of the package, implementation issues, scope, limitations, and future extensions of the software are addressed. A survey is given of related algorithms and symbolic software to compute exact solutions of nonlinear differential equations.
KeywordsExact solutions, Nonlinear PDEs, Tanh method, Symbolic software
URL http://www.sciencedirect.com/science/article/pii/S0747717104000082
JournalJournal of Symbolic Computation
Pages669 - 705
Translation No
Refereed No