Intrinsic geometry and wave-breaking phenomena in solutions of the Camassa-Holm equation
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913612292947968 |
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| author | Freire, Igor Leite |
| author_facet | Freire, Igor Leite |
| contents | Pseudospherical surfaces determined by Cauchy problems involving the Camassa-Holm equation are considered herein. We study how global solutions influence the corresponding surface, as well as we investigate two sorts of singularities of the metric: the first one is just when the co-frame of dual form is not linearly independent. The second sort of singularity is that arising from solutions blowing up. In particular, it is shown that the metric blows up if and only if the solution breaks in finite time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18941 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Intrinsic geometry and wave-breaking phenomena in solutions of the Camassa-Holm equation Freire, Igor Leite Analysis of PDEs Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems 35A01, 58J60, 37K40, 35Q51 Pseudospherical surfaces determined by Cauchy problems involving the Camassa-Holm equation are considered herein. We study how global solutions influence the corresponding surface, as well as we investigate two sorts of singularities of the metric: the first one is just when the co-frame of dual form is not linearly independent. The second sort of singularity is that arising from solutions blowing up. In particular, it is shown that the metric blows up if and only if the solution breaks in finite time. |
| title | Intrinsic geometry and wave-breaking phenomena in solutions of the Camassa-Holm equation |
| topic | Analysis of PDEs Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems 35A01, 58J60, 37K40, 35Q51 |
| url | https://arxiv.org/abs/2310.18941 |