On solitary waves for the Korteweg--de Vries equation on metric star graphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909105117986816 |
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| author | Mugnolo, Delio Noja, Diego Seifert, Christian |
| author_facet | Mugnolo, Delio Noja, Diego Seifert, Christian |
| contents | We study the Korteweg--de Vries equation on a metric star graph and investigate existence of solitary waves on the metric graph in terms of the coefficients of the equation on each edge, the coupling condition at the central vertex of the star and the speeds of the travelling wave. We show that, with a continuity condition at the vertex, solitary waves can occur exactly when the parameters are chosen in a fairly special manner. We also consider coupling conditions beyond continuity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On solitary waves for the Korteweg--de Vries equation on metric star graphs Mugnolo, Delio Noja, Diego Seifert, Christian Analysis of PDEs We study the Korteweg--de Vries equation on a metric star graph and investigate existence of solitary waves on the metric graph in terms of the coefficients of the equation on each edge, the coupling condition at the central vertex of the star and the speeds of the travelling wave. We show that, with a continuity condition at the vertex, solitary waves can occur exactly when the parameters are chosen in a fairly special manner. We also consider coupling conditions beyond continuity. |
| title | On solitary waves for the Korteweg--de Vries equation on metric star graphs |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.08368 |