BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS FOR THE ONE-DIMENSIONAL GENERALIZED BENJAMIN-BONA-MAHONY EQUATION

Guoxiang Luo (P. R. China) and Shengqiang Tang (P. R. China)

Received January 28, 2008

Abstract

By using the bifurcation theory of dynamical systems to the one-dimensional generalized Benjamin-Bona-Mahony equation, the existence of solitary wave solutions, periodic cusp wave solutions and uncountably infinite many smooth and nonsmooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of the above waves are determined.

Keywords and phrases: solitary wave solution, periodic cusp wave solutions, periodic wave solution, the one-dimensional generalized Benjamin-Bona-Mahony equation.