Some Interesting Bifurcations of Nonlinear Waves for the Generalized Drinfel’d-Sokolov System
We study the bifurcations of nonlinear waves for the generalized Drinfel’d-Sokolov system ut+(vm)x=0,vt+a(vn)xxx+buxv+cuvx=0 called D(m,n) system. We reveal some interesting bifurcation phenomena as follows. (1) For D(2,1) system, the fractional solitary waves can be bifurcated from the trigonometri...
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/189486 |
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| author | Huixian Cai Chaohong Pan Zhengrong Liu |
| author_facet | Huixian Cai Chaohong Pan Zhengrong Liu |
| author_sort | Huixian Cai |
| collection | DOAJ |
| description | We study the bifurcations of nonlinear waves for the generalized Drinfel’d-Sokolov system ut+(vm)x=0,vt+a(vn)xxx+buxv+cuvx=0 called D(m,n) system. We reveal some interesting bifurcation phenomena as follows. (1) For D(2,1) system, the fractional solitary waves can be bifurcated from the trigonometric periodic waves and the elliptic periodic waves, and the kink waves can be bifurcated from the solitary waves and the singular waves. (2) For D(1,2) system, the compactons can be bifurcated from the solitary waves, and the peakons can be bifurcated from the solitary waves and the singular cusp waves. (3) For D(2,2) system, the solitary waves can be bifurcated from the smooth periodic waves and the singular periodic waves. |
| format | Article |
| id | doaj-art-8c448f3ada434baf8eb5927f7744b484 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8c448f3ada434baf8eb5927f7744b4842025-02-03T05:59:07ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/189486189486Some Interesting Bifurcations of Nonlinear Waves for the Generalized Drinfel’d-Sokolov SystemHuixian Cai0Chaohong Pan1Zhengrong Liu2Department of Mathematics, South China University of Technology, Guangzhou 510640, ChinaDepartment of Mathematics, South China University of Technology, Guangzhou 510640, ChinaDepartment of Mathematics, South China University of Technology, Guangzhou 510640, ChinaWe study the bifurcations of nonlinear waves for the generalized Drinfel’d-Sokolov system ut+(vm)x=0,vt+a(vn)xxx+buxv+cuvx=0 called D(m,n) system. We reveal some interesting bifurcation phenomena as follows. (1) For D(2,1) system, the fractional solitary waves can be bifurcated from the trigonometric periodic waves and the elliptic periodic waves, and the kink waves can be bifurcated from the solitary waves and the singular waves. (2) For D(1,2) system, the compactons can be bifurcated from the solitary waves, and the peakons can be bifurcated from the solitary waves and the singular cusp waves. (3) For D(2,2) system, the solitary waves can be bifurcated from the smooth periodic waves and the singular periodic waves.http://dx.doi.org/10.1155/2014/189486 |
| spellingShingle | Huixian Cai Chaohong Pan Zhengrong Liu Some Interesting Bifurcations of Nonlinear Waves for the Generalized Drinfel’d-Sokolov System Abstract and Applied Analysis |
| title | Some Interesting Bifurcations of Nonlinear Waves for the Generalized Drinfel’d-Sokolov System |
| title_full | Some Interesting Bifurcations of Nonlinear Waves for the Generalized Drinfel’d-Sokolov System |
| title_fullStr | Some Interesting Bifurcations of Nonlinear Waves for the Generalized Drinfel’d-Sokolov System |
| title_full_unstemmed | Some Interesting Bifurcations of Nonlinear Waves for the Generalized Drinfel’d-Sokolov System |
| title_short | Some Interesting Bifurcations of Nonlinear Waves for the Generalized Drinfel’d-Sokolov System |
| title_sort | some interesting bifurcations of nonlinear waves for the generalized drinfel d sokolov system |
| url | http://dx.doi.org/10.1155/2014/189486 |
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