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Zbl 0880.35105
Berloff, Natalia G.; Howard, Louis N.
Solitary and periodic solutions of nonlinear nonintegrable equations. (English)
[J] Stud. Appl. Math. 99, No.1, 1-24 (1997). ISSN 0022-2526; ISSN 1467-9590/e

Summary: The singular manifold method and partial fraction decomposition allow one to find some special solutions of nonintegrable partial differential equations (PDE) in the form of solitary waves, traveling wave fronts, and periodic pulse trains. The truncated Painlevé expansion is used to reduce a nonlinear PDE to a multilinear form. Some special solutions of the latter equation represent solitary waves and traveling wave fronts of the original PDE. The partial fraction decomposition is used to obtain a periodic wave train solution as an infinite superposition of the ``corrected'' solitary waves.

MSC 2000:: *35Q53 KdV-like equations
35Q51 Solitons

Keywords: singular manifold method; partial fraction decomposition; nonintegrable partial differential equations; solitary waves; traveling wave fronts; periodic pulse trains

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