A higher order system of some coupled nonlinear Schr\"odinger and Korteweg-de Vries equations

TL;DR

This paper proves the existence and multiplicity of solutions for a complex coupled nonlinear Schrödinger and Korteweg-de Vries system, expanding understanding of such higher-order nonlinear PDEs.

Contribution

It introduces new existence and multiplicity results for a bi-harmonic coupled Schrödinger-KdV system under specific parameter conditions.

Findings

Existence of bound state solutions

Multiplicity of ground state solutions

Conditions on parameters for solutions

Abstract

We prove existence and multiplicity of bound and ground state solutions, under appropriate conditions on the parameters, for a bi-harmonic stationary system of coupled nonlinear Schr\"odinger--Korteweg-de Vries equations.