Bifurcations of traveling wave solutions of a (3+1)-dimensional nonlinear model generated by the Jaulent-Miodek hierarchy

We study bifurcation of traveling wave solutions of a class of (3+1)-dimensional nonlinear evolution equations generated by the Jaulent-Miodek hierarchy. We obtain phase portraits of the nonlinear transformation system according to the different bifurcation regions of parameters. Different kinds of traveling wave solutions, such as the periodic wave solutions, solitary wave solutions, kink wave solutions and anti-kink wave solutions are found to exist under certain parameter conditions, and the exact solutions of traveling waves are obtained