Symbolic methods to construct exact solutions of nonlinear partial differential equations

Willy Hereman and Ameina Nuseir

Mathematics and Computers in Simulation (MATCOM), 1997, vol. 43, issue 1, 13-27

Abstract: Two straightforward methods for finding solitary-wave and soliton solutions are presented and applied to a variety of nonlinear partial differential equations. The first method is a simplied version of Hirota's method. It is shown to be an effective tool to explicitly construct. multi-soliton solutions of completely integrable evolution equations of fifth-order, including the Kaup-Kupershmidt equation for which the soliton solutions were not previously known. The second technique is the truncated Painlevé expansion method or singular manifold method. It is used to find closed-form solitary-wave solutions of the Fitzhugh-Nagumo equation with convection term, and an evolution equation due to Calogero. Since both methods are algorithmic, they can be implemented in the language of any symbolic manipulation program.

Date: 1997
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:43:y:1997:i:1:p:13-27

DOI: 10.1016/S0378-4754(96)00053-5

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