Periodic and solitary wave solutions of the long wave-short wave Yajima-Oikawa-Newell model

TL;DR

This paper analyzes the Yajima-Oikawa-Newell model, an integrable system describing long wave-short wave interactions, and constructs explicit periodic and solitary wave solutions along with conservation laws.

Contribution

It introduces the Yajima-Oikawa-Newell model with arbitrary coupling constants and derives new periodic and solitary wave solutions, expanding understanding of wave interactions.

Findings

Constructed families of periodic wave solutions.

Derived solitary wave solutions.

Identified conservation laws for the model.

Abstract

Models describing long wave-short wave resonant interactions have many physical applications from fluid dynamics to plasma physics. We consider here the Yajima-Oikawa-Newell (YON) model, which has been recently introduced combining the interaction terms of two long wave-short wave, integrable models, one proposed by Yajima-Oikawa, and the other one by Newell. The new YON model contains two arbitrary coupling constants and it is still integrable - in the sense of possessing a Lax pair - for any values of these coupling constants. It reduces to the Yajima-Oikawa or the Newell systems for special choices of these two parameters. We construct families of periodic and solitary wave solutions, which display the generation of very long waves. We also compute the explicit expression of a number of conservation laws.