Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation
We study the bifurcation phenomena of nonlinear waves described by a generalized Zakharov-Kuznetsov equation ut+au2+bu4ux+γuxxx+δuxyy=0. We reveal four kinds of interesting bifurcation phenomena. The first kind is that the low-kink waves can be bifurcated from the symmetric solitary waves, the 1-b...
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Wiley
2013-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2013/812120 |
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| author | Yun Wu Zhengrong Liu |
| author_facet | Yun Wu Zhengrong Liu |
| author_sort | Yun Wu |
| collection | DOAJ |
| description | We study the bifurcation phenomena of nonlinear waves described by a generalized Zakharov-Kuznetsov
equation ut+au2+bu4ux+γuxxx+δuxyy=0. We reveal four kinds of interesting bifurcation phenomena. The first kind is that the low-kink waves can be bifurcated from the symmetric solitary waves,
the 1-blow-up waves, the tall-kink waves, and the antisymmetric solitary waves. The second kind is that the 1-blow-up waves can be bifurcated from the periodic-blow-up waves, the symmetric solitary waves, and the 2-blow-up waves. The third kind is that the periodic-blow-up waves can be bifurcated from the symmetric periodic waves. The fourth kind is that the tall-kink waves can be bifurcated from the symmetric periodic waves. |
| format | Article |
| id | doaj-art-964b299c380f434fb2e91ff0107fb041 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-964b299c380f434fb2e91ff0107fb0412025-02-03T01:06:14ZengWileyAdvances in Mathematical Physics1687-91201687-91392013-01-01201310.1155/2013/812120812120Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov EquationYun Wu0Zhengrong Liu1Department of Mathematics and Computer Science, Guizhou Normal University, Guiyang, Guizhou 550001, ChinaDepartment of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, ChinaWe study the bifurcation phenomena of nonlinear waves described by a generalized Zakharov-Kuznetsov equation ut+au2+bu4ux+γuxxx+δuxyy=0. We reveal four kinds of interesting bifurcation phenomena. The first kind is that the low-kink waves can be bifurcated from the symmetric solitary waves, the 1-blow-up waves, the tall-kink waves, and the antisymmetric solitary waves. The second kind is that the 1-blow-up waves can be bifurcated from the periodic-blow-up waves, the symmetric solitary waves, and the 2-blow-up waves. The third kind is that the periodic-blow-up waves can be bifurcated from the symmetric periodic waves. The fourth kind is that the tall-kink waves can be bifurcated from the symmetric periodic waves.http://dx.doi.org/10.1155/2013/812120 |
| spellingShingle | Yun Wu Zhengrong Liu Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation Advances in Mathematical Physics |
| title | Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation |
| title_full | Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation |
| title_fullStr | Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation |
| title_full_unstemmed | Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation |
| title_short | Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation |
| title_sort | bifurcation phenomena of nonlinear waves in a generalized zakharov kuznetsov equation |
| url | http://dx.doi.org/10.1155/2013/812120 |
| work_keys_str_mv | AT yunwu bifurcationphenomenaofnonlinearwavesinageneralizedzakharovkuznetsovequation AT zhengrongliu bifurcationphenomenaofnonlinearwavesinageneralizedzakharovkuznetsovequation |