Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach

TL;DR

This paper investigates soliton solutions of the two-component Zakharov-Yajima-Oikawa system using Madelung's fluid approach, revealing interactions between bright and dark solitons under resonance conditions.

Contribution

It introduces a Madelung fluid framework to derive one-soliton solutions and analyzes soliton interactions in the integrable ZYO system under resonance.

Findings

Derived one-soliton solutions using Madelung's approach

Analyzed interactions between bright and dark solitons

Reduced complex interactions to a one-component system

Abstract

Using the multiple scales method, the interaction between two bright and one dark solitons is studied. Provided that a long wave-short wave resonance condition is satisfied, the two-component Zakharov-Yajima-Oikawa (ZYO) completely integrable system is obtained. By using a Madelung fluid description, the one-soliton solutions of the corresponding ZYO system are determined. Furthermore, a discussion on the interaction between one bright and two dark solitons is presented. In particular, this problem is reduced to solve a one-component ZYO system in the resonance conditions.