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Popular ansatz methods and solitary wave solutions of the Kuramoto-Sivashinsky equation

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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.

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Authors and Affiliations

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

    N. A. Kudryashov & M. B. Soukharev

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  1. N. A. Kudryashov
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  2. M. B. Soukharev
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Correspondence to N. A. Kudryashov.

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Kudryashov, N.A., Soukharev, M.B. Popular ansatz methods and solitary wave solutions of the Kuramoto-Sivashinsky equation. Regul. Chaot. Dyn. 14, 407–419 (2009). https://doi.org/10.1134/S1560354709030046

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