Multiple Non-radial Solutions for Coupled Schr\"{o}dinger Equations

TL;DR

This paper proves the existence of infinitely many non-radial positive and nodal solutions for an N-coupled nonlinear elliptic system under certain symmetry and coupling conditions.

Contribution

It introduces new methods to establish the existence of multiple non-radial solutions in coupled Schrödinger systems, expanding understanding beyond radial solutions.

Findings

Existence of infinite non-radial positive solutions

Existence of infinite non-radial nodal solutions

Solutions are symmetric under rotation

Abstract

The paper deals with the existence of non-radial solutions for an $N$-coupled nonlinear elliptic system. In the repulsive regime with some structure conditions on the coupling and for each symmetric subspace of rotation symmetry, we prove the existence of an infinite sequence of non-radial positive solutions and an infinite sequence of non-radial nodal solutions.