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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2406.09184 |
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| _version_ | 1866910633914531840 |
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| author | Ingimarson, Benjamin Pego, Robert L. |
| author_facet | Ingimarson, Benjamin Pego, Robert L. |
| contents | We prove the existence of small solitary waves for one-dimensional lattices of particles that each repel every other particle with a force that decays as a power of distance. For force exponents $α+1$ with $\frac43<α<3$, we employ fixed-point arguments to find near-sonic solitary waves having scaled velocity profiles close to non-degenerate solitary-wave profiles of fractional KdV or generalized Benjamin-Ono equations. These equations were recently found to approximately govern unidirectional long-wave motions in these lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09184 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of solitary waves in particle lattices with power-law forces Ingimarson, Benjamin Pego, Robert L. Pattern Formation and Solitons Analysis of PDEs Classical Analysis and ODEs Primary 37K40, 70F45, Secondary 37K60, 70H09, 35R11 We prove the existence of small solitary waves for one-dimensional lattices of particles that each repel every other particle with a force that decays as a power of distance. For force exponents $α+1$ with $\frac43<α<3$, we employ fixed-point arguments to find near-sonic solitary waves having scaled velocity profiles close to non-degenerate solitary-wave profiles of fractional KdV or generalized Benjamin-Ono equations. These equations were recently found to approximately govern unidirectional long-wave motions in these lattices. |
| title | Existence of solitary waves in particle lattices with power-law forces |
| topic | Pattern Formation and Solitons Analysis of PDEs Classical Analysis and ODEs Primary 37K40, 70F45, Secondary 37K60, 70H09, 35R11 |
| url | https://arxiv.org/abs/2406.09184 |