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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2411.08428 |
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| _version_ | 1866915017609183232 |
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| author | Caputo, Sabrina Vaira, Giusi |
| author_facet | Caputo, Sabrina Vaira, Giusi |
| contents | In this paper we consider the existence of standing waves for a coupled system of $k$ equations with Lotka-Volterra type interaction. We prove the existence of a standing wave solution with all nontrivial components satisfying a prescribed asymptotic profile. In particular, the $k-1$-last components of such solution exhibits a concentrating behavior, while the first one keeps a quantum nature. We analyze first in detail the result with three equations since this is the first case in which the coupling has a role contrary to what happens when only two densities appear. We also discuss the existence of solutions of this form for systems with other kind of couplings making a comparison with Lotka-Volterra type systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08428 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partially concentrating solutions for systems with Lotka-Volterra type interactions Caputo, Sabrina Vaira, Giusi Analysis of PDEs In this paper we consider the existence of standing waves for a coupled system of $k$ equations with Lotka-Volterra type interaction. We prove the existence of a standing wave solution with all nontrivial components satisfying a prescribed asymptotic profile. In particular, the $k-1$-last components of such solution exhibits a concentrating behavior, while the first one keeps a quantum nature. We analyze first in detail the result with three equations since this is the first case in which the coupling has a role contrary to what happens when only two densities appear. We also discuss the existence of solutions of this form for systems with other kind of couplings making a comparison with Lotka-Volterra type systems. |
| title | Partially concentrating solutions for systems with Lotka-Volterra type interactions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.08428 |