Solitary wave solutions to the Isobe-Kakinuma model for water waves
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866910815355928576 |
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| author | Colin, Mathieu Iguchi, Tatsuo |
| author_facet | Colin, Mathieu Iguchi, Tatsuo |
| contents | We consider the Isobe-Kakinuma model for two-dimensional water waves in the case of the flat bottom. The Isobe-Kakinuma model is a system of Euler-Lagrange equations for a Lagrangian approximating Luke's Lagrangian for water waves. We show theoretically the existence of a family of small amplitude solitary wave solutions to the Isobe-Kakinuma model in the long wave regime. Numerical analysis for large amplitude solitary wave solutions is also provided and suggests the existence of a solitary wave of extreme form with a sharp crest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_06481 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Solitary wave solutions to the Isobe-Kakinuma model for water waves Colin, Mathieu Iguchi, Tatsuo Analysis of PDEs We consider the Isobe-Kakinuma model for two-dimensional water waves in the case of the flat bottom. The Isobe-Kakinuma model is a system of Euler-Lagrange equations for a Lagrangian approximating Luke's Lagrangian for water waves. We show theoretically the existence of a family of small amplitude solitary wave solutions to the Isobe-Kakinuma model in the long wave regime. Numerical analysis for large amplitude solitary wave solutions is also provided and suggests the existence of a solitary wave of extreme form with a sharp crest. |
| title | Solitary wave solutions to the Isobe-Kakinuma model for water waves |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1910.06481 |