Exact soliton solutions and long-time asymptotics of the Yajima-Oikawa equation via Riemann-Hilbert approach

TL;DR

This paper derives exact soliton solutions and analyzes the long-time behavior of the Yajima-Oikawa equation using Riemann-Hilbert techniques, providing insights into ion sound wave propagation influenced by high-frequency Langmuir waves.

Contribution

It introduces a Riemann-Hilbert framework for the Yajima-Oikawa equation, obtaining explicit soliton solutions and asymptotic descriptions for long-time dynamics.

Findings

Exact soliton solutions derived from Riemann-Hilbert problem

Long-time asymptotics formulated in Zakharov-Manakov region

Application of Deift-Zhou steepest descent method

Abstract

The Yajima-Oikawa equation is a deformation of the Zakharov equation which models the propagation of ion sound waves subject to the ponderomotive force induced by high-frequency Langmuir waves. In this work, we study the exact soliton solutions and long-time asymptotics of the Yajima-Oikawa equation by Riemann-Hilbert approach. The Riemann-Hilbert problem is formulated in terms of two reflection coefficients determined by the initial condition. Then exact soliton solutions associated with the Yajima-Oikawa equation are obtained based on this Riemann-Hilbert problem. Finally, the long-time asymptotics of solution to the Yajima-Oikawa equation in Zakharov-Manakov region is formulated by Deift-Zhou nonlinear steepest descent method.