Bifurcation Method to Analysis of Traveling Wave Solutions for (3+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy (Journal of Partial Differential Equations, 2020)
In this paper, the third model of four (3+1)-dimensional nonlinear evolutionequations, 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 differentbifurcation regions, we obtain kink (anti-kink) wave solutions, solitary wave solutionsand periodic wave solutions for the third of these models in the different subsets of4-parameters space by dynamical system method. Furthermore, the explicit exact expressions of these bounded traveling waves are obtained. All these wave solutions arecharacterized by distinct physical structures.
Keywords: Nonlinear (3+1)-dimensional equation; Bifurcation method; traveling wave solution.