Peakon solutions and analytical properties for the Camassa-Holm type equations with quadratic nonlinearities
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911700738899968 |
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| author | Chen, Yonghong Qiao, Zhijun Zhu, Mingxuan |
| author_facet | Chen, Yonghong Qiao, Zhijun Zhu, Mingxuan |
| contents | In this paper, we derive the multi-peakon dynamical system of a class of Camassa-Holm-type equations with quadratic nonlinearities. We also consider the analytical properties for the Cauchy problem. Firstly, we establish local well-posedness of solutions in Besov spaces and then provide the blow-up criteria. Subsequently, we impose appropriate sufficient conditions on the initial data to guaranty that the corresponding solution either exists globally or blows up in a finite time. Finally, we prove the ill-posedness in the Besov space $B_{2,\infty}^{3/2}$ by utilizing the non-traveling wave solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20773 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Peakon solutions and analytical properties for the Camassa-Holm type equations with quadratic nonlinearities Chen, Yonghong Qiao, Zhijun Zhu, Mingxuan Analysis of PDEs 35Q35 (Primary) 35A01, 35B44, 46E35 (Secondary) In this paper, we derive the multi-peakon dynamical system of a class of Camassa-Holm-type equations with quadratic nonlinearities. We also consider the analytical properties for the Cauchy problem. Firstly, we establish local well-posedness of solutions in Besov spaces and then provide the blow-up criteria. Subsequently, we impose appropriate sufficient conditions on the initial data to guaranty that the corresponding solution either exists globally or blows up in a finite time. Finally, we prove the ill-posedness in the Besov space $B_{2,\infty}^{3/2}$ by utilizing the non-traveling wave solutions. |
| title | Peakon solutions and analytical properties for the Camassa-Holm type equations with quadratic nonlinearities |
| topic | Analysis of PDEs 35Q35 (Primary) 35A01, 35B44, 46E35 (Secondary) |
| url | https://arxiv.org/abs/2605.20773 |