Residual Symmetry Reduction and Consistent Riccati Expansion to a Nonlinear Evolution Equation
The residual symmetry of a (1 + 1)-dimensional nonlinear evolution equation (NLEE) ut+uxxx−6u2ux+6λux=0 is obtained through Painlevé expansion. By introducing a new dependent variable, the residual symmetry is localized into Lie point symmetry in an enlarged system, and the related symmetry reductio...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/6503564 |
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| author | Lamine Thiam Xi-zhong Liu |
| author_facet | Lamine Thiam Xi-zhong Liu |
| author_sort | Lamine Thiam |
| collection | DOAJ |
| description | The residual symmetry of a (1 + 1)-dimensional nonlinear evolution equation (NLEE) ut+uxxx−6u2ux+6λux=0 is obtained through Painlevé expansion. By introducing a new dependent variable, the residual symmetry is localized into Lie point symmetry in an enlarged system, and the related symmetry reduction solutions are obtained using the standard Lie symmetry method. Furthermore, the (1 + 1)-dimensional NLEE equation is proved to be integrable in the sense of having a consistent Riccati expansion (CRE), and some new Bäcklund transformations (BTs) are given. In addition, some explicitly expressed solutions including interaction solutions between soliton and cnoidal waves are derived from these BTs. |
| format | Article |
| id | doaj-art-dce3c8ddbaf1423b99c13ae0ef7ac5ea |
| institution | OA Journals |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-dce3c8ddbaf1423b99c13ae0ef7ac5ea2025-08-20T02:21:37ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/65035646503564Residual Symmetry Reduction and Consistent Riccati Expansion to a Nonlinear Evolution EquationLamine Thiam0Xi-zhong Liu1Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, ChinaInstitute of Nonlinear Science, Shaoxing University, Shaoxing 312000, ChinaThe residual symmetry of a (1 + 1)-dimensional nonlinear evolution equation (NLEE) ut+uxxx−6u2ux+6λux=0 is obtained through Painlevé expansion. By introducing a new dependent variable, the residual symmetry is localized into Lie point symmetry in an enlarged system, and the related symmetry reduction solutions are obtained using the standard Lie symmetry method. Furthermore, the (1 + 1)-dimensional NLEE equation is proved to be integrable in the sense of having a consistent Riccati expansion (CRE), and some new Bäcklund transformations (BTs) are given. In addition, some explicitly expressed solutions including interaction solutions between soliton and cnoidal waves are derived from these BTs.http://dx.doi.org/10.1155/2019/6503564 |
| spellingShingle | Lamine Thiam Xi-zhong Liu Residual Symmetry Reduction and Consistent Riccati Expansion to a Nonlinear Evolution Equation Complexity |
| title | Residual Symmetry Reduction and Consistent Riccati Expansion to a Nonlinear Evolution Equation |
| title_full | Residual Symmetry Reduction and Consistent Riccati Expansion to a Nonlinear Evolution Equation |
| title_fullStr | Residual Symmetry Reduction and Consistent Riccati Expansion to a Nonlinear Evolution Equation |
| title_full_unstemmed | Residual Symmetry Reduction and Consistent Riccati Expansion to a Nonlinear Evolution Equation |
| title_short | Residual Symmetry Reduction and Consistent Riccati Expansion to a Nonlinear Evolution Equation |
| title_sort | residual symmetry reduction and consistent riccati expansion to a nonlinear evolution equation |
| url | http://dx.doi.org/10.1155/2019/6503564 |
| work_keys_str_mv | AT laminethiam residualsymmetryreductionandconsistentriccatiexpansiontoanonlinearevolutionequation AT xizhongliu residualsymmetryreductionandconsistentriccatiexpansiontoanonlinearevolutionequation |