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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.15645 |
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| _version_ | 1866909697931476992 |
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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 |