Ground states for a system of nonlinear Schrodinger equations with three waves interaction

TL;DR

This paper investigates the existence of vector ground state solutions in a system of nonlinear Schrödinger equations involving three-wave interactions, highlighting the conditions under which all three components are non-zero.

Contribution

It introduces the concept of vector ground states with all components non-zero for a three-wave interaction Schrödinger system, expanding understanding of such solutions.

Findings

Existence of vector ground states with all components non-zero.

Conditions for the existence of three-wave interaction ground states.

Extension of ground state theory to multi-component nonlinear Schrödinger systems.

Abstract

We consider a system of nonlinear Schrodinger equations with three waves interaction studying the existence of ground state solutions. In particular, we find a vector ground state, namely a ground state with the three components all different from zero.