Bifurcation of Traveling Wave Solutions for (2+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy-Reference-Cited by-同舟云学术

Bifurcation of Traveling Wave Solutions for (2+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy

Published:2015 Issue: Volume:2015 Page:1-14
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Ran Yanping¹²,Li Jing¹,Li Xin¹^ORCID,Tian Zheng¹

Affiliation:

1. College of Applied Science, Beijing University of Technology, Beijing 100124, China

2. School of Mathematics and Statistics, Tianshui Normal University, Tianshui, Gansu 741001, China

Abstract

Four (2+1)-dimensional nonlinear evolution equations, generated by the Jaulent-Miodek hierarchy, are investigated by the bifurcation method of planar dynamical systems. The bifurcation regions in different subsets of the parameters space are obtained. According to the different phase portraits in different regions, we obtain kink (antikink) wave solutions, solitary wave solutions, and periodic wave solutions for the third of these models by dynamical system method. Furthermore, the explicit exact expressions of these bounded traveling waves are obtained. All these wave solutions obtained are characterized by distinct physical structures.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2015/820916.pdf

Reference12 articles.

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4. Symmetry reductions and exact solutions of the (2 + 1)-dimensional Jaulent–Miodek equation