TY - JOUR
T1 - Bifurcation Method to Analysis of Traveling Wave Solutions for (3+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy
AU - Ran , Yanping
AU - Li , Jing
JO - Journal of Partial Differential Equations
VL - 4
SP - 304
EP - 321
PY - 2019
DA - 2019/01
SN - 31
DO - http://doi.org/10.4208/jpde.v31.n4.2
UR - https://global-sci.org/intro/article_detail/jpde/12945.html
KW - Nonlinear (3+1)-dimensional equation
KW - Bifurcation method
KW - traveling wave solution.
AB - <p>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.</p>