Normalized solution to coupled nonhomogeneous nonlinear elliptic system with three wave interaction under unbounded potentials

TL;DR

This paper establishes the existence of normalized solutions for a coupled three-wave nonlinear Schrödinger system with unbounded potentials using variational methods under 2-norm constraints.

Contribution

It introduces a novel variational approach to find normalized solutions for a complex coupled wave system with asymmetric coercive potentials.

Findings

Existence of solutions under 2-norm constraints

Application of variational methods to coupled nonlinear Schrödinger systems

Handling of unbounded potentials in the analysis

Abstract

In this paper, we use the variational method to find the normalized solutions of the quadratic coupled three wave Schrodinger equation with asymmetric coercive potential. We prove the existence of solutions for the system with 2-norm constraints.