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Main Authors: Wang, Deng-Shan, Yang, Yingmin, Zhu, Xiaodong
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2507.15645
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author Wang, Deng-Shan
Yang, Yingmin
Zhu, Xiaodong
author_facet Wang, Deng-Shan
Yang, Yingmin
Zhu, Xiaodong
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_15645
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Exact soliton solutions and long-time asymptotics of the Yajima-Oikawa equation via Riemann-Hilbert approach
Wang, Deng-Shan
Yang, Yingmin
Zhu, Xiaodong
Exactly Solvable and Integrable Systems
Mathematical Physics
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.
title Exact soliton solutions and long-time asymptotics of the Yajima-Oikawa equation via Riemann-Hilbert approach
topic Exactly Solvable and Integrable Systems
Mathematical Physics
url https://arxiv.org/abs/2507.15645