Exact Jacobi elliptic solutions of the $abcd$-system
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913245245210624 |
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| author | Daniels, Jake Nguyen, Nghiem V. |
| author_facet | Daniels, Jake Nguyen, Nghiem V. |
| contents | In this manuscript, consideration is given to the existence of periodic traveling-wave solutions to the $abcd$-system. This system was derived by Bona, Saut, and Chen to describe small amplitude, long wavelength gravity waves on the surface of water. These exact solutions are formulated in terms of the Jacobi elliptic function cnoidal. The existence of explicit traveling-wave solutions is very useful in theoretical investigations such as stability of solutions, as well as other numerical analysis of the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16756 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact Jacobi elliptic solutions of the $abcd$-system Daniels, Jake Nguyen, Nghiem V. Analysis of PDEs 35A16, 35A24, 35B10 In this manuscript, consideration is given to the existence of periodic traveling-wave solutions to the $abcd$-system. This system was derived by Bona, Saut, and Chen to describe small amplitude, long wavelength gravity waves on the surface of water. These exact solutions are formulated in terms of the Jacobi elliptic function cnoidal. The existence of explicit traveling-wave solutions is very useful in theoretical investigations such as stability of solutions, as well as other numerical analysis of the system. |
| title | Exact Jacobi elliptic solutions of the $abcd$-system |
| topic | Analysis of PDEs 35A16, 35A24, 35B10 |
| url | https://arxiv.org/abs/2402.16756 |