Two Expanding Integrable Models of the Geng-Cao Hierarchy
As far as linear integrable couplings are concerned, one has obtained some rich and interesting results. In the paper, we will deduce two kinds of expanding integrable models of the Geng-Cao (GC) hierarchy by constructing different 6-dimensional Lie algebras. One expanding integrable model (actually...
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Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/860935 |
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doaj-9da7ac8b6779443ebbe9989a4552a7602020-11-24T23:39:26ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/860935860935Two Expanding Integrable Models of the Geng-Cao HierarchyXiurong Guo0Yufeng Zhang1Xuping Zhang2Department of Basic Courses, Shandong University of Science and Technology, Tai’an, Shandong 271019, ChinaCollege of Science, China University of Mining and Technology, Xuzhou 221116, ChinaDepartment of Basic Courses, Shandong University of Science and Technology, Tai’an, Shandong 271019, ChinaAs far as linear integrable couplings are concerned, one has obtained some rich and interesting results. In the paper, we will deduce two kinds of expanding integrable models of the Geng-Cao (GC) hierarchy by constructing different 6-dimensional Lie algebras. One expanding integrable model (actually, it is a nonlinear integrable coupling) reduces to a generalized Burgers equation and further reduces to the heat equation whose expanding nonlinear integrable model is generated. Another one is an expanding integrable model which is different from the first one. Finally, the Hamiltonian structures of the two expanding integrable models are obtained by employing the variational identity and the trace identity, respectively.http://dx.doi.org/10.1155/2014/860935 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Xiurong Guo Yufeng Zhang Xuping Zhang |
| spellingShingle |
Xiurong Guo Yufeng Zhang Xuping Zhang Two Expanding Integrable Models of the Geng-Cao Hierarchy Abstract and Applied Analysis |
| author_facet |
Xiurong Guo Yufeng Zhang Xuping Zhang |
| author_sort |
Xiurong Guo |
| title |
Two Expanding Integrable Models of the Geng-Cao Hierarchy |
| title_short |
Two Expanding Integrable Models of the Geng-Cao Hierarchy |
| title_full |
Two Expanding Integrable Models of the Geng-Cao Hierarchy |
| title_fullStr |
Two Expanding Integrable Models of the Geng-Cao Hierarchy |
| title_full_unstemmed |
Two Expanding Integrable Models of the Geng-Cao Hierarchy |
| title_sort |
two expanding integrable models of the geng-cao hierarchy |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2014-01-01 |
| description |
As far as linear integrable couplings are concerned, one has obtained some rich and
interesting results. In the paper, we will deduce two kinds of expanding integrable models of the Geng-Cao (GC) hierarchy by constructing different 6-dimensional Lie algebras. One expanding integrable model (actually, it is a nonlinear integrable coupling) reduces to a generalized Burgers equation and further reduces to the heat equation whose expanding nonlinear integrable model is generated. Another one is an expanding integrable model which is different from the first one. Finally, the Hamiltonian structures of the two expanding integrable models are obtained by employing the variational identity and the trace identity, respectively. |
| url |
http://dx.doi.org/10.1155/2014/860935 |
| work_keys_str_mv |
AT xiurongguo twoexpandingintegrablemodelsofthegengcaohierarchy AT yufengzhang twoexpandingintegrablemodelsofthegengcaohierarchy AT xupingzhang twoexpandingintegrablemodelsofthegengcaohierarchy |
| _version_ |
1725513647360311296 |