Existence and stability of solitary waves to the rotation-Camassa-Holm equation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916250724073472 |
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| author | Tong, Hao Yang, Shaojie |
| author_facet | Tong, Hao Yang, Shaojie |
| contents | In this paper, we investigate existence and stability of solitary waves to the rotation-Camassa-Holm equation which can be considered as a model in the shallow water for the long-crested waves propagating near the equator with effect of the Coriolis force due to the Earths rotation. We prove existence of solitary waves by performing a phase plane analysis. Moreover, utilizing the approach proposed by Grillakis-Shatah-Strauss, we prove stability of solitary waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00631 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Existence and stability of solitary waves to the rotation-Camassa-Holm equation Tong, Hao Yang, Shaojie Analysis of PDEs 35Q35, 35Q51 In this paper, we investigate existence and stability of solitary waves to the rotation-Camassa-Holm equation which can be considered as a model in the shallow water for the long-crested waves propagating near the equator with effect of the Coriolis force due to the Earths rotation. We prove existence of solitary waves by performing a phase plane analysis. Moreover, utilizing the approach proposed by Grillakis-Shatah-Strauss, we prove stability of solitary waves. |
| title | Existence and stability of solitary waves to the rotation-Camassa-Holm equation |
| topic | Analysis of PDEs 35Q35, 35Q51 |
| url | https://arxiv.org/abs/2305.00631 |