In this paper we consider the existence of standing waves for a coupled system of k equa- tions with Lotka–Volterra type interaction. We prove the existence of a standing wave so- lution with all nontrivial components satisfying a prescribed asymptotic profile. In particu- lar, 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 sys- tems with other kind of couplings making a comparison with Lotka–Volterra type systems.
Partially concentrating solutions for systems with Lotka-Volterra type interactions
Sabrina Caputo;Giusi Vaira
2026-01-01
Abstract
In this paper we consider the existence of standing waves for a coupled system of k equa- tions with Lotka–Volterra type interaction. We prove the existence of a standing wave so- lution with all nontrivial components satisfying a prescribed asymptotic profile. In particu- lar, 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 sys- tems with other kind of couplings making a comparison with Lotka–Volterra type systems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
