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arXiv · 2411.08428

Partially concentrating solutions for systems with Lotka-Volterra type interactions

Sabrina Caputo·Giusi Vaira
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Abstract

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.

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Sabrina Caputo, Giusi Vaira. 2024-11-13. Partially concentrating solutions for systems with Lotka-Volterra type interactions. https://arxiv.org/abs/2411.08428

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