Bifurcations and Parametric Representations of Peakon, Solitary Wave and Smooth Periodic Wave Solutions for a Two-Component Degasperis-Procesi Equation

摘要

By using the bifurcation method of dynamical systems and the method of phase portraits analysis, we consider a two-component Degasperis-Procesi equation:mt=-3mux-mxu+kρρx,ρt=-ρxu+2ρux, the existence of the peakon, solitary wave and smooth periodic wave is proved, and exact parametric representations of above travelling wave solutions are obtained in different parameter regions.