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28 March 2024
 
  » arxiv » nlin.SI/0504053

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Meromorphic traveling wave solutions of the Kuramoto-Sivashinsky equation
Alexandre Eremenko ;
Date 25 Apr 2005
Subject Exactly Solvable and Integrable Systems; Complex Variables | nlin.SI math.CV
AbstractWe determine all cases when there exists a meromorphic solution of the third order ODE describing traveling waves solutions of the Kuramoto-Sivashinsky equation. It turns out that there are no other meromorphic solutions besides those explicit solutions found by Kuramoto and Kudryashov. The general method used in this paper, based on Nevanlinna theory, is applicable to finding all meromorphic solutions of a wide class of non-linear ODE. Keywords: Kuramoto and Sivashinsky equation, meromorphic functions, elliptic functions, Nevanlinna theory.
Source arXiv, nlin.SI/0504053
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