Periodically modulated solitary waves of the CH-KP-I equation
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909216712687616 |
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| author | Nilsson, Dag Seth, Douglas Svensson Wang, Yuexun |
| author_facet | Nilsson, Dag Seth, Douglas Svensson Wang, Yuexun |
| contents | We consider the CH-KP-I equation. For this equation we prove the existence of steady solutions, which are solitary in one horizontal direction and periodic in the other. We show that such waves bifurcate from the line solitary wave solutions, i.e. solitary wave solutions to the Camassa-Holm equation, in a dimension-breaking bifurcation. This is achieved through reformulating the problem as a dynamical system for a perturbation of the line solitary wave solutions, where the periodic direction takes the role of time, then applying the Lyapunov-Iooss theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02423 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Periodically modulated solitary waves of the CH-KP-I equation Nilsson, Dag Seth, Douglas Svensson Wang, Yuexun Analysis of PDEs 76B15, 76B45, 35Q35 We consider the CH-KP-I equation. For this equation we prove the existence of steady solutions, which are solitary in one horizontal direction and periodic in the other. We show that such waves bifurcate from the line solitary wave solutions, i.e. solitary wave solutions to the Camassa-Holm equation, in a dimension-breaking bifurcation. This is achieved through reformulating the problem as a dynamical system for a perturbation of the line solitary wave solutions, where the periodic direction takes the role of time, then applying the Lyapunov-Iooss theorem. |
| title | Periodically modulated solitary waves of the CH-KP-I equation |
| topic | Analysis of PDEs 76B15, 76B45, 35Q35 |
| url | https://arxiv.org/abs/2406.02423 |