On the well-posedness of a nonlocal (two-place) FORQ equation via a two-component peakon system
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916548780752896 |
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| author | Karlsen, Kenneth Rybalko, Yan |
| author_facet | Karlsen, Kenneth Rybalko, Yan |
| contents | We investigate the Cauchy problem for a nonlocal (two-place) FORQ equation. By interpreting this equation as a special case of a two-component peakon system (exhibiting a cubic nonlinearity), we convert the Cauchy problem into a system of ordinary differential equations in a Banach space. Using this approach, we are able to demonstrate local well-posedness in the Sobolev space $H^{s}$ where $s > 5/2$. We also establish the continuity properties for the data-to-solution map for a range of Sobolev spaces. Finally, we briefly explore the relationship between the two-component system and the bi-Hamiltonian AKNS hierarchy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_14850 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the well-posedness of a nonlocal (two-place) FORQ equation via a two-component peakon system Karlsen, Kenneth Rybalko, Yan Analysis of PDEs We investigate the Cauchy problem for a nonlocal (two-place) FORQ equation. By interpreting this equation as a special case of a two-component peakon system (exhibiting a cubic nonlinearity), we convert the Cauchy problem into a system of ordinary differential equations in a Banach space. Using this approach, we are able to demonstrate local well-posedness in the Sobolev space $H^{s}$ where $s > 5/2$. We also establish the continuity properties for the data-to-solution map for a range of Sobolev spaces. Finally, we briefly explore the relationship between the two-component system and the bi-Hamiltonian AKNS hierarchy. |
| title | On the well-posedness of a nonlocal (two-place) FORQ equation via a two-component peakon system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2305.14850 |