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Regular and Chaotic Dynamics, 2009, Volume 14, Issue 3, Pages 407–419
DOI: https://doi.org/10.1134/S1560354709030046 (Mi rcd589) 		 
This article is cited in 52 scientific papers (total in 52 papers)

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
Citations (52)
DOI: https://doi.org/10.1134/S1560354709030046
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.
Received: 12.03.2009
Accepted: 04.05.2009
Bibliographic databases:
Document Type: Article
MSC: 34A05, 34A25, 34M05, 35C05
Language: English
Citation: N. A. Kudryashov, M. B. Soukharev, “Popular Ansatz Methods and Solitary Wave Solutions of the Kuramoto–Sivashinsky Equation”, Regul. Chaotic Dyn., 14:3 (2009), 407–419
Citation in format AMSBIB
\Bibitem{KudSou09}
\by N. A. Kudryashov, M. B. Soukharev
\paper Popular Ansatz Methods and Solitary Wave Solutions of the Kuramoto–Sivashinsky Equation
\jour Regul. Chaotic Dyn.
\yr 2009
\vol 14
\issue 3
\pages 407--419
\mathnet{http://mi.mathnet.ru/rcd589}
\crossref{https://doi.org/10.1134/S1560354709030046}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2525621}
\zmath{https://zbmath.org/?q=an:1229.34008}
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