N. A. Kudryashov, M. B. Soukharev, “Popular Ansatz Methods and Solitary Wave Solutions of the Kuramoto–Sivashinsky Equation”, Regul. Chaotic Dyn., 2009, Volume 14, Issue 3,Pages <nobr>407

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Popular Ansatz Methods and Solitary Wave Solutions of the Kuramoto–Sivashinsky Equation

N. A. Kudryashov, M. B. Soukharev

Department of Applied Mathematics, Moscow Engineering and Physics Institute, Kashirskoe sh. 31, Moscow 115409, Russia

Abstract: Some methods to look for exact solutions of nonlinear differential equations are discussed. It is shown that many popular methods are equivalent to each other. Several recent publications with "new" solitary wave solutions for the Kuramoto–Sivashinsky equation are analyzed. We demonstrate that all these solutions coincide with the known ones.

Keywords: Kuramoto–Sivashinsky equation, $(G'/G)$-method, Tanh-method, Exp-function method.

MSC: 34A05, 34A25, 34M05, 35C05

Received: 12.03.2009
Accepted: 04.05.2009

Language: English

DOI: 10.1134/S1560354709030046