On a two-component Camassa-Holm equation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916509137240064 |
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| author | Zhang, Zixing Liu, Q. P. |
| author_facet | Zhang, Zixing Liu, Q. P. |
| contents | A two-component generalization of the Camassa-Holm equation and its reduction proposed recently by Xue, Du and Geng [Appl. Math. Lett. {\bf 146} (2023) 108795] are studied. For this two-component equation, its missing bi-Hamiltonian structure is constructed and a Miura transformation is introduced so that it may be regarded as a modification of the very first two-component Camassa-Holm equation. %[Phys. Rev. E {\bf 53} (1996) ; Lett. Math. Phys. {\bf 53 } (2006)]. Using a proper reciprocal transformation, a particular reduction of this two-component equation, which admits $N-$ peakon solution, is brought to the celebrated Burgers equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_04124 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a two-component Camassa-Holm equation Zhang, Zixing Liu, Q. P. Exactly Solvable and Integrable Systems A two-component generalization of the Camassa-Holm equation and its reduction proposed recently by Xue, Du and Geng [Appl. Math. Lett. {\bf 146} (2023) 108795] are studied. For this two-component equation, its missing bi-Hamiltonian structure is constructed and a Miura transformation is introduced so that it may be regarded as a modification of the very first two-component Camassa-Holm equation. %[Phys. Rev. E {\bf 53} (1996) ; Lett. Math. Phys. {\bf 53 } (2006)]. Using a proper reciprocal transformation, a particular reduction of this two-component equation, which admits $N-$ peakon solution, is brought to the celebrated Burgers equation. |
| title | On a two-component Camassa-Holm equation |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2412.04124 |