Meromorphic Traveling Wave Solutions of the Kuramoto-Sivashinsky Equation
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 $\nu w''' + bw''+\mu w'+w^2/2+A=0$. 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.