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Volume 31, Issue 4
Bifurcation Method to Analysis of Traveling Wave Solutions for (3+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy

Yanping Ran & Jing Li

DOI: 10.4208/jpde.v31.n4.2

J. Part. Diff. Eq., 31 (2018), pp. 304-321.

Published online: 2019-01

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  • 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.

  • Keywords

Nonlinear (3+1)-dimensional equation Bifurcation method traveling wave solution.

  • AMS Subject Headings

37H20, 35C07, 37J20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ranypmath@163.com (Yanping Ran)

ijing@bjut.edu.cn (Jing Li)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-31-304, author = {Ran , Yanping and Li , Jing}, title = {Bifurcation Method to Analysis of Traveling Wave Solutions for (3+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy}, journal = {Journal of Partial Differential Equations}, year = {2019}, volume = {31}, number = {4}, pages = {304--321}, 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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v31.n4.2}, url = {http://global-sci.org/intro/article_detail/jpde/12945.html} }
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 -

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.

Ran , Yanping and Li , Jing. (2019). 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. 31 (4). 304-321. doi:10.4208/jpde.v31.n4.2
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