Residual Symmetry, Bäcklund Transformation, and Soliton Solutions of the Higher-Order Broer-Kaup System
Under investigation in this paper is the higher-order Broer-Kaup(HBK) system, which describes the bidirectional propagation of long waves in shallow water. Via the standard truncated Painlevé expansion method, the residual symmetry of this system is derived. By introducing an appropriate auxiliary-d...
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| Format: | Article |
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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/9975303 |
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| author | Yarong Xia Ruoxia Yao Xiangpeng Xin |
| author_facet | Yarong Xia Ruoxia Yao Xiangpeng Xin |
| author_sort | Yarong Xia |
| collection | DOAJ |
| description | Under investigation in this paper is the higher-order Broer-Kaup(HBK) system, which describes the bidirectional propagation of long waves in shallow water. Via the standard truncated Painlevé expansion method, the residual symmetry of this system is derived. By introducing an appropriate auxiliary-dependent variable, the residual symmetry is successfully localized to Lie point symmetries. Via solving the initial value problems, the finite symmetry transformations are presented. However, the solution which obtained from the residual symmetry is a special group invariant solutions. In order to find more general solution of HBK system, we further generalize the residual symmetry method to the consistent tanh expansion (CTE) method and prove that the HBK system is CTE solvable, then the resonant soliton solutions and interaction solutions among different nonlinear excitations are obtained by the CET method. |
| format | Article |
| id | doaj-art-6e76ce437fa4401ab9364d0c4e9c7a90 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-6e76ce437fa4401ab9364d0c4e9c7a902025-02-03T06:43:48ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/99753039975303Residual Symmetry, Bäcklund Transformation, and Soliton Solutions of the Higher-Order Broer-Kaup SystemYarong Xia0Ruoxia Yao1Xiangpeng Xin2School of Computer Science, Shaanxi Normal University, Xi’an 710062, ChinaSchool of Computer Science, Shaanxi Normal University, Xi’an 710062, ChinaSchool of Mathematical Sciences, Liaocheng University, Liaocheng 252029, ChinaUnder investigation in this paper is the higher-order Broer-Kaup(HBK) system, which describes the bidirectional propagation of long waves in shallow water. Via the standard truncated Painlevé expansion method, the residual symmetry of this system is derived. By introducing an appropriate auxiliary-dependent variable, the residual symmetry is successfully localized to Lie point symmetries. Via solving the initial value problems, the finite symmetry transformations are presented. However, the solution which obtained from the residual symmetry is a special group invariant solutions. In order to find more general solution of HBK system, we further generalize the residual symmetry method to the consistent tanh expansion (CTE) method and prove that the HBK system is CTE solvable, then the resonant soliton solutions and interaction solutions among different nonlinear excitations are obtained by the CET method.http://dx.doi.org/10.1155/2021/9975303 |
| spellingShingle | Yarong Xia Ruoxia Yao Xiangpeng Xin Residual Symmetry, Bäcklund Transformation, and Soliton Solutions of the Higher-Order Broer-Kaup System Advances in Mathematical Physics |
| title | Residual Symmetry, Bäcklund Transformation, and Soliton Solutions of the Higher-Order Broer-Kaup System |
| title_full | Residual Symmetry, Bäcklund Transformation, and Soliton Solutions of the Higher-Order Broer-Kaup System |
| title_fullStr | Residual Symmetry, Bäcklund Transformation, and Soliton Solutions of the Higher-Order Broer-Kaup System |
| title_full_unstemmed | Residual Symmetry, Bäcklund Transformation, and Soliton Solutions of the Higher-Order Broer-Kaup System |
| title_short | Residual Symmetry, Bäcklund Transformation, and Soliton Solutions of the Higher-Order Broer-Kaup System |
| title_sort | residual symmetry backlund transformation and soliton solutions of the higher order broer kaup system |
| url | http://dx.doi.org/10.1155/2021/9975303 |
| work_keys_str_mv | AT yarongxia residualsymmetrybacklundtransformationandsolitonsolutionsofthehigherorderbroerkaupsystem AT ruoxiayao residualsymmetrybacklundtransformationandsolitonsolutionsofthehigherorderbroerkaupsystem AT xiangpengxin residualsymmetrybacklundtransformationandsolitonsolutionsofthehigherorderbroerkaupsystem |