Bifurcation Method to Analysis of Traveling Wave Solutions for (3+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy

Abstract

In this paper, the third model of four (3+1)-dimensional nonlinear evolution equations, generated by the Jaulent-Miodek hierarchy, is investigated by the bifurcation method of planar dynamical systems. The 2-parameters different bifurcation regions are obtained. According to the different phase portraits in 2-parameters different bifurcation regions, we obtain kink (anti-kink) wave solutions, solitary wave solutions and periodic wave solutions for the third of these models in the different subsets of 4-parameters space by dynamical system method. Furthermore, the explicit exact expressions of these bounded traveling waves are obtained. All these wave solutions are characterized by distinct physical structures.