Bifurcation of travelling wave solutions for a [formula omitted]-dimensional nonlinear dispersive long wave equation

Abstract

The bifurcation method of planar dynamical systems and numerical simulation method of differential equations are employed to investigate the ( 2 + 1 ) -dimensional nonlinear dispersive long wave equation. We obtain the parameter bifurcation sets that divide the parameter space into different regions which correspond to qualitatively different phase portraits. In different regions, different types of travelling solutions including solitary wave solutions, shock wave solutions and periodical wave solutions are obtained. Furthermore, the explicit exact expressions of these bounded travelling waves are obtained.