Solitary and periodic solutions of nonlinear nonintegrable equations

Natalia G. Berloff, Louis N. Howard

Research output: Contribution to journalArticlepeer-review

52 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalStudies in Applied Mathematics
Issue number1
Publication statusPublished - Jul 1997
Externally publishedYes


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