Existence of bound states for (N+1)-coupled long-wave--short-wave interaction equations

TL;DR

This paper proves the existence of infinitely many smooth positive bound states in a system modeling the interaction between multiple short waves and a long wave, relevant in physics and fluid dynamics.

Contribution

It establishes the existence of an infinite family of bound states for (N+1)-coupled long-wave--short-wave equations, a novel result in this area.

Findings

Existence of infinitely many bound states proven

Bound states are smooth and positive

Applicable to physics and fluid dynamics models

Abstract

We prove the existence of an infinite family of smooth positive bound states for (N +1)-coupled long-wave--short-wave interaction equations. The system describes the interaction between N short waves and a long wave and is of interest in physics and fluid dynamics.