Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.08428 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of 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.