Symmetry, Pulson Solution, and Conservation Laws of the Holm-Hone Equation
In this paper, we focus on the Holm-Hone equation which is a fifth-order generalization of the Camassa-Holm equation. It was shown that this equation is not integrable due to the nonexistence of a suitable Lagrangian or bi-Hamiltonian structure and negative results from Painlevé analysis and the Wah...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/4364108 |
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| author | Guo Wang Xuelin Yong Yehui Huang Jing Tian |
| author_facet | Guo Wang Xuelin Yong Yehui Huang Jing Tian |
| author_sort | Guo Wang |
| collection | DOAJ |
| description | In this paper, we focus on the Holm-Hone equation which is a fifth-order generalization of the Camassa-Holm equation. It was shown that this equation is not integrable due to the nonexistence of a suitable Lagrangian or bi-Hamiltonian structure and negative results from Painlevé analysis and the Wahlquist-Estabrook method. We mainly study its symmetry properties, travelling wave solutions, and conservation laws. The symmetry group and its one-dimensional optimal system are given. Furthermore, preliminary classifications of its symmetry reductions are investigated. Also we derive some solitary pattern solutions and nonanalytic first-order pulson solution via the ansatz-based method. Finally, some conservation laws for the fifth-order equation are presented. |
| format | Article |
| id | doaj-art-ef3a4af934d1455dba5c2e99c4d7c0ab |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-ef3a4af934d1455dba5c2e99c4d7c0ab2025-02-03T05:45:31ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/43641084364108Symmetry, Pulson Solution, and Conservation Laws of the Holm-Hone EquationGuo Wang0Xuelin Yong1Yehui Huang2Jing Tian3Department of Basic Courses, Yuncheng Polytechnic College, Yuncheng, Shanxi 044000, ChinaSchool of Mathematical Sciences and Physics, North China Electric Power University, Beijing 102206, ChinaSchool of Mathematical Sciences and Physics, North China Electric Power University, Beijing 102206, ChinaDepartment of Mathematics, Towson University, Towson, MD 21252, USAIn this paper, we focus on the Holm-Hone equation which is a fifth-order generalization of the Camassa-Holm equation. It was shown that this equation is not integrable due to the nonexistence of a suitable Lagrangian or bi-Hamiltonian structure and negative results from Painlevé analysis and the Wahlquist-Estabrook method. We mainly study its symmetry properties, travelling wave solutions, and conservation laws. The symmetry group and its one-dimensional optimal system are given. Furthermore, preliminary classifications of its symmetry reductions are investigated. Also we derive some solitary pattern solutions and nonanalytic first-order pulson solution via the ansatz-based method. Finally, some conservation laws for the fifth-order equation are presented.http://dx.doi.org/10.1155/2019/4364108 |
| spellingShingle | Guo Wang Xuelin Yong Yehui Huang Jing Tian Symmetry, Pulson Solution, and Conservation Laws of the Holm-Hone Equation Advances in Mathematical Physics |
| title | Symmetry, Pulson Solution, and Conservation Laws of the Holm-Hone Equation |
| title_full | Symmetry, Pulson Solution, and Conservation Laws of the Holm-Hone Equation |
| title_fullStr | Symmetry, Pulson Solution, and Conservation Laws of the Holm-Hone Equation |
| title_full_unstemmed | Symmetry, Pulson Solution, and Conservation Laws of the Holm-Hone Equation |
| title_short | Symmetry, Pulson Solution, and Conservation Laws of the Holm-Hone Equation |
| title_sort | symmetry pulson solution and conservation laws of the holm hone equation |
| url | http://dx.doi.org/10.1155/2019/4364108 |
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