Meromorphic Traveling Wave Solutions of the Kuramoto-Sivashinsky Equation


  • Alexandre Eremenko Purdue University 150 N University Str., West Lafayette IN 47907-2067, USA

Ключові слова:

Kuramoto and Sivashinsky equation, meromorphic functions, elliptic functions, Nevanlinna theory.


We determine all cases when there exists a meromorphic solution of the ODE
nw''' + bw'' + mw' + w2/2+ A = 0. This equation describes 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 nonlinear ODE.

Mathematics Subject Classification: 35Q20, 34A20.


Як цитувати

Eremenko, A. Meromorphic Traveling Wave Solutions of the Kuramoto-Sivashinsky Equation. Журн. мат. фіз. анал. геом. 2006, 2, 278-286.





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