Solutions and Bifurcations of a class of (3+1)-dimensional Nonlinear Models generated by the Jaulent-Miodek hierarchy equation
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- 英文论文题名：Solutions and Bifurcations of a class of (3+1)-dimensional Nonlinear Models generated by the Jaulent-Miodek hierarchy equation
- 论文作者：CHAI Song-hao ; HE Bin ; LI Jing
- 英文论文作者：CHAI Song-hao ; HE Bin ; LI Jing ; College of Applied Sciences ; Beijing University of Technology
- 年：2016
- 作者机构：College of Applied Sciences;Beijing University of Technology;
- 英文论文关键词：(3+1)-dimensional nonlinear evolution equation ; Bifurcation theory ; Exact traveling wave solutions ; Numerical simulations
- 会议召开时间：2016-05-06
- 会议录名称：第十届动力学与控制学术会议摘要集
- 语种：英文
- 分类号：O175
- 学会代码：AGLU
- 会议名称：第十届动力学与控制学术会议
- 会议地点：中国四川成都
- 主办单位：中国力学学会动力学与控制专业委员会
- 学会名称：中国力学学会
- 页数：2
- 文件大小：770k
- 原文格式：D
- 会议级别：全国
摘要
In this paper,the(3+1)-dimensional nonlinear evolution equation:w_t=2(w_(xx)-2w~3)-3/4(_x~(-1))w_(yy)-2w_x_x~(-1)w_y)-3/4_x~(-1)w_(zz)-1/4w_z-1/2w_ygenerated by the Jaulent-Miodek hierarchy,is investigated by the bifurcation theory of dynamical systems.Focusing on the problems,the research are as follows:(1)By using the traveling wave transformation,the(3+l)-dimensional nonlinear model generated by the Jaulent-Miodek hierarchy is changed to a system of ordinary differential systems.And we analyze the equilibrium bifurcation of the transformation system.(2)By using the theory of dynamical systems,we get the dynamical behavior of the nonlinear transformation system.According to the different bifurcation regions of parameters,we obtain the phase portraits of the nonlinear transformation system.(3)Through calculating we obtain all periodic wave solutions,solitary wave solutions,kink wave solutions and anti-kink wave solutions of the(3+1)-dimensional nonlinear evolution equations and obtain the exact expressions of these bounded traveling wave solutions.And we have the waveform graphs of the Jaulent-Miodek model by using the Maple Software.
In this paper,the(3+1)-dimensional nonlinear evolution equation:w_t=2(w_xx-2w~3)_x-3/4(_x~(-1))w_(xy)-2w_x_x~(-1)w_y-6ww_y)-3/4_x~(-1)w_(zz)-1/4w_x-1/2w_y generated by the Jaulent-Miodek hierarchy,is investigated by the bifurcation theory of dynamical systems.Focusing on the problems,the research are as follows:(1) By using the traveling wave transformation,the(3+1)-dimensional nonlinear model generated by the Jaulent-Miodek hierarchy is changed to a system of ordinary differential systems.And we analyze the equilibrium bifurcation of the transformation system.(2) By using the theory of dynamical systems,we get the dynamical behavior of the nonlinear transformation system.According to the different bifurcation regions of parameters,we obtain the phase portraits of the nonlinear transformation system.(3) Through calculating we obtain all periodic wave solutions,solitary wave solutions,kink wave solutions and anti-kink wave solutions of the(3+1)-dimensional nonlinear evolution equations and obtain the exact expressions of these bounded traveling wave solutions.And we have the waveform graphs of the Jaulent-Miodek model by using the Maple Software.
In this paper,the(3+1)-dimensional nonlinear evolution equation:w_t=2(w_xx-2w~3)_x-3/4(_x~(-1))w_(xy)-2w_x_x~(-1)w_y-6ww_y)-3/4_x~(-1)w_(zz)-1/4w_x-1/2w_y generated by the Jaulent-Miodek hierarchy,is investigated by the bifurcation theory of dynamical systems.Focusing on the problems,the research are as follows:(1) By using the traveling wave transformation,the(3+1)-dimensional nonlinear model generated by the Jaulent-Miodek hierarchy is changed to a system of ordinary differential systems.And we analyze the equilibrium bifurcation of the transformation system.(2) By using the theory of dynamical systems,we get the dynamical behavior of the nonlinear transformation system.According to the different bifurcation regions of parameters,we obtain the phase portraits of the nonlinear transformation system.(3) Through calculating we obtain all periodic wave solutions,solitary wave solutions,kink wave solutions and anti-kink wave solutions of the(3+1)-dimensional nonlinear evolution equations and obtain the exact expressions of these bounded traveling wave solutions.And we have the waveform graphs of the Jaulent-Miodek model by using the Maple Software.
引文