EXACT TRAVELLING WAVE SOLUTIONS FOR THE GENERALIZED KURAMOTO-SIVASHINSKY EQUATION

Abstract

By using transformation , 2 3 2 1 u a u a a u + + = ′ ′ the method of sine-cosine and the method of dynamical bifurcation theory of the differentiable dynamics, we study the generalized Kuramoto-Sivashinsky equation. It is shown that the generalized Kuramoto-Sivashinsky equation gives solitary wave solution, solitary patterns wave solution, and periodic wave solution. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. All exact explicit parametric representations of the above waves are determined.