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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2501.02719 |
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| _version_ | 1866915092066467840 |
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| author | Yang, Zhenzhen Liu, Huan Shen, Jing |
| author_facet | Yang, Zhenzhen Liu, Huan Shen, Jing |
| contents | We delve into the inverse scattering transform of the real-valued vector modified Korteweg--de Vries equation, emphasizing the challenges posed by $N$ pairs of higher-order poles in the transmission coefficient and the enhanced spectral symmetry stemming from real-valued constraints. Utilizing the generalized vector cross product, we formulate an $(n+1)\times(n+1)$ matrix-valued Riemann--Hilbert problem to tackle the complexities inherent in multi-component systems. We subsequently demonstrate the existence and uniqueness of solutions for a singularity-free equivalent problem, adeptly handling the intricacies of multiple poles. In reflectionless cases, we reconstruct multi-pole soliton solutions through a system of linear algebraic equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02719 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Real-Valued Vector Modified Korteweg--de Vries Equation: Solitons Featuring Multiple Poles Yang, Zhenzhen Liu, Huan Shen, Jing Pattern Formation and Solitons We delve into the inverse scattering transform of the real-valued vector modified Korteweg--de Vries equation, emphasizing the challenges posed by $N$ pairs of higher-order poles in the transmission coefficient and the enhanced spectral symmetry stemming from real-valued constraints. Utilizing the generalized vector cross product, we formulate an $(n+1)\times(n+1)$ matrix-valued Riemann--Hilbert problem to tackle the complexities inherent in multi-component systems. We subsequently demonstrate the existence and uniqueness of solutions for a singularity-free equivalent problem, adeptly handling the intricacies of multiple poles. In reflectionless cases, we reconstruct multi-pole soliton solutions through a system of linear algebraic equations. |
| title | Real-Valued Vector Modified Korteweg--de Vries Equation: Solitons Featuring Multiple Poles |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2501.02719 |