Numerical study of the Amick-Schonbek system
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929281843593216 |
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| author | Klein, C. Saut, J. -C. |
| author_facet | Klein, C. Saut, J. -C. |
| contents | The aim of this paper is to present a survey and a detailed numerical study on a remarkable Boussinesq system describing weakly nonlinear, long surface water waves. In the one-dimensional case, this system can be viewed as a dispersive perturbation of the hyperbolic Saint-Venant (shallow water) system. The asymptotic stability of the solitary waves is numerically established. Blow-up of solutions for initial data not satisfying the non-cavitation condition as well as the appearence of dispersive shock waves are studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17517 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Numerical study of the Amick-Schonbek system Klein, C. Saut, J. -C. Analysis of PDEs The aim of this paper is to present a survey and a detailed numerical study on a remarkable Boussinesq system describing weakly nonlinear, long surface water waves. In the one-dimensional case, this system can be viewed as a dispersive perturbation of the hyperbolic Saint-Venant (shallow water) system. The asymptotic stability of the solitary waves is numerically established. Blow-up of solutions for initial data not satisfying the non-cavitation condition as well as the appearence of dispersive shock waves are studied. |
| title | Numerical study of the Amick-Schonbek system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2311.17517 |