Polygons for finding exact solutions of nonlinear differential equations

2006/01/16 by Nikolay A. Kudryashov, Nikolai A. Kudryashov, Kudryashov, Nikolai A. +2
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #Numerical methods for differential equations #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0601035

16 pages, 2 figures

arxiv created 2006/01/16 · openalex publication_date 2006/01/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

New method for finding exact solutions of nonlinear differential equations is presented. It is based on constructing the polygon corresponding to the equation studied. The algorithms of power geometry are used. The method is applied for finding one -- parameter exact solutions of the generalized Korteveg -- de Vries -- Burgers equation, the generalized Kuramoto - Sivashinsky equation, and the fifth -- order nonlinear evolution equation. All these nonlinear equations contain the term u^mu_x. New exact solitary waves are found.

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