CRE Solvability, Exact Soliton-Cnoidal Wave Interaction Solutions, and Nonlocal Symmetry for the Modified Boussinesq Equation
It is proved that the modified Boussinesq equation is consistent Riccati expansion (CRE) solvable; two types of special soliton-cnoidal wave interaction solution of the equation are explicitly given, which is difficult to be found by other traditional methods. Moreover, the nonlocal symmetry related...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/4874392 |
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| author | Wenguang Cheng Biao Li |
| author_facet | Wenguang Cheng Biao Li |
| author_sort | Wenguang Cheng |
| collection | DOAJ |
| description | It is proved that the modified Boussinesq equation is consistent Riccati expansion (CRE) solvable; two types of special soliton-cnoidal wave interaction solution of the equation are explicitly given, which is difficult to be found by other traditional methods. Moreover, the nonlocal symmetry related to the consistent tanh expansion (CTE) and the residual symmetry from the truncated Painlevé expansion, as well as the relationship between them, are obtained. The residual symmetry is localized after embedding the original system in an enlarged one. The symmetry group transformation of the enlarged system is derived by applying the Lie point symmetry approach. |
| format | Article |
| id | doaj-art-d484c55bfaee4ece8c60dcb1ef467401 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-d484c55bfaee4ece8c60dcb1ef4674012025-02-03T05:45:44ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/48743924874392CRE Solvability, Exact Soliton-Cnoidal Wave Interaction Solutions, and Nonlocal Symmetry for the Modified Boussinesq EquationWenguang Cheng0Biao Li1Department of Mathematics, Yuxi Normal University, Yuxi 653100, ChinaNingbo Collaborative Innovation Center of Nonlinear Hazard System of Ocean and Atmosphere, Ningbo University, Ningbo 315211, ChinaIt is proved that the modified Boussinesq equation is consistent Riccati expansion (CRE) solvable; two types of special soliton-cnoidal wave interaction solution of the equation are explicitly given, which is difficult to be found by other traditional methods. Moreover, the nonlocal symmetry related to the consistent tanh expansion (CTE) and the residual symmetry from the truncated Painlevé expansion, as well as the relationship between them, are obtained. The residual symmetry is localized after embedding the original system in an enlarged one. The symmetry group transformation of the enlarged system is derived by applying the Lie point symmetry approach.http://dx.doi.org/10.1155/2016/4874392 |
| spellingShingle | Wenguang Cheng Biao Li CRE Solvability, Exact Soliton-Cnoidal Wave Interaction Solutions, and Nonlocal Symmetry for the Modified Boussinesq Equation Advances in Mathematical Physics |
| title | CRE Solvability, Exact Soliton-Cnoidal Wave Interaction Solutions, and Nonlocal Symmetry for the Modified Boussinesq Equation |
| title_full | CRE Solvability, Exact Soliton-Cnoidal Wave Interaction Solutions, and Nonlocal Symmetry for the Modified Boussinesq Equation |
| title_fullStr | CRE Solvability, Exact Soliton-Cnoidal Wave Interaction Solutions, and Nonlocal Symmetry for the Modified Boussinesq Equation |
| title_full_unstemmed | CRE Solvability, Exact Soliton-Cnoidal Wave Interaction Solutions, and Nonlocal Symmetry for the Modified Boussinesq Equation |
| title_short | CRE Solvability, Exact Soliton-Cnoidal Wave Interaction Solutions, and Nonlocal Symmetry for the Modified Boussinesq Equation |
| title_sort | cre solvability exact soliton cnoidal wave interaction solutions and nonlocal symmetry for the modified boussinesq equation |
| url | http://dx.doi.org/10.1155/2016/4874392 |
| work_keys_str_mv | AT wenguangcheng cresolvabilityexactsolitoncnoidalwaveinteractionsolutionsandnonlocalsymmetryforthemodifiedboussinesqequation AT biaoli cresolvabilityexactsolitoncnoidalwaveinteractionsolutionsandnonlocalsymmetryforthemodifiedboussinesqequation |