High energy solutions of quadratic coupling Schrodinger equation with nonconstant potential

TL;DR

This paper investigates high energy solutions of a quadratic coupled Schrödinger system with nonconstant potential using variational and perturbation methods, analyzing their asymptotic behavior as coupling diminishes.

Contribution

It introduces a novel application of variational and perturbation techniques to find high energy solutions in a coupled Schrödinger system with asymmetric potential.

Findings

Existence of high energy solutions established

Asymptotic behavior characterized as coupling coefficient approaches zero

Methodology applicable to similar nonlinear quantum systems

Abstract

In this paper, we use the variational method, especially the perturbation method, to find the perturbed high energy solutions of the quadratic coupled Schrodinger system with asymmetric asymptotic potential and their asymptotic behavior as the coupling coefficient converges to 0.