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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:nlin/0201008 (nlin)
[Submitted on 8 Jan 2002 (v1), last revised 16 Nov 2003 (this version, v3)]

Title:Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs

Authors:D. Baldwin, U. Goktas, W. Hereman, L. Hong, R. S. Martino, J. Miller
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Abstract: Algorithms 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 Jacobi's 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, Jacobi's sn or cn functions. Examples illustrate key steps of the algorithms.
The new algorithms are implemented in Mathematica. The package DDESpecialSolutions.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.
Comments: 39 pages. Software available from Willy Hereman's home page at this http URL
Subjects: Exactly Solvable and Integrable Systems (nlin.SI)
Cite as: arXiv:nlin/0201008 [nlin.SI]
  (or arXiv:nlin/0201008v3 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.nlin/0201008

Submission history

From: Douglas Baldwin [view email]
[v1] Tue, 8 Jan 2002 03:07:16 UTC (51 KB)
[v2] Mon, 7 Apr 2003 09:13:15 UTC (49 KB)
[v3] Sun, 16 Nov 2003 18:22:08 UTC (39 KB)
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