Bifurcation of Traveling Wave Solutions for (2+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy
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 di...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/820916 |
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| _version_ | 1850173091166027776 |
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| author | Yanping Ran Jing Li Xin Li Zheng Tian |
| author_facet | Yanping Ran Jing Li Xin Li Zheng Tian |
| author_sort | Yanping Ran |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d12309b7a1a3480389c7f9dd30d269d4 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d12309b7a1a3480389c7f9dd30d269d42025-08-20T02:19:55ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/820916820916Bifurcation of Traveling Wave Solutions for (2+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek HierarchyYanping Ran0Jing Li1Xin Li2Zheng Tian3College of Applied Science, Beijing University of Technology, Beijing 100124, ChinaCollege of Applied Science, Beijing University of Technology, Beijing 100124, ChinaCollege of Applied Science, Beijing University of Technology, Beijing 100124, ChinaCollege of Applied Science, Beijing University of Technology, Beijing 100124, ChinaFour (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.http://dx.doi.org/10.1155/2015/820916 |
| spellingShingle | Yanping Ran Jing Li Xin Li Zheng Tian Bifurcation of Traveling Wave Solutions for (2+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy Abstract and Applied Analysis |
| title | Bifurcation of Traveling Wave Solutions for (2+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy |
| title_full | Bifurcation of Traveling Wave Solutions for (2+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy |
| title_fullStr | Bifurcation of Traveling Wave Solutions for (2+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy |
| title_full_unstemmed | Bifurcation of Traveling Wave Solutions for (2+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy |
| title_short | Bifurcation of Traveling Wave Solutions for (2+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy |
| title_sort | bifurcation of traveling wave solutions for 2 1 dimensional nonlinear models generated by the jaulent miodek hierarchy |
| url | http://dx.doi.org/10.1155/2015/820916 |
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