The Quasi-Integrability of a Generalized Camassa-Holm Equation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929610544906240 |
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| author | Guo, Mingyue Shi, Zhenhua |
| author_facet | Guo, Mingyue Shi, Zhenhua |
| contents | This paper examines a generalization of the Camassa-Holm equation from the perspective of integrability. Using the framework developed by Dubrovin on bi-Hamiltonian deformations and the general theory of quasi-integrability, we demonstrate that a unique bi-Hamiltonian structure is possible for this generalized equation only when it reduces to the original CH equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01260 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Quasi-Integrability of a Generalized Camassa-Holm Equation Guo, Mingyue Shi, Zhenhua Exactly Solvable and Integrable Systems Mathematical Physics This paper examines a generalization of the Camassa-Holm equation from the perspective of integrability. Using the framework developed by Dubrovin on bi-Hamiltonian deformations and the general theory of quasi-integrability, we demonstrate that a unique bi-Hamiltonian structure is possible for this generalized equation only when it reduces to the original CH equation. |
| title | The Quasi-Integrability of a Generalized Camassa-Holm Equation |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2412.01260 |