Meromorphic traveling wave solutions of the Kuramoto-Sivashinsky equation

Details Meromorphic traveling wave solutions of the Kuramoto-Sivashinsky equation Meromorphic traveling wave solutions of the Kuramoto-Sivashinsky equation

2005-04-25

arxiv.org/abs/nlin/0504053v1

J. Math. Phys., Anal. Geom. 2 (2006) N 3 278-286

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages

Scientific paper

We 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.

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