Genus two KdV soliton gases and their long-time asymptotics
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911572550483968 |
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| author | Wang, Deng-Shan Zhu, Dinghao Zhu, Xiaodong |
| author_facet | Wang, Deng-Shan Zhu, Dinghao Zhu, Xiaodong |
| contents | This paper employs the Riemann-Hilbert problem to provide a comprehensive analysis of the asymptotic behavior of the high-genus Korteweg-de Vries soliton gases. It is demonstrated that the two-genus soliton gas is related to the two-phase Riemann-Theta function as \(x \to +\infty\), and approaches to zero as \(x \to -\infty\). Additionally, the long-time asymptotic behavior of this two-genus soliton gas can be categorized into five distinct regions in the \(x\)-\(t\) plane, which from left to right are rapidly decay, modulated one-phase wave, unmodulated one-phase wave, modulated two-phase wave, and unmodulated two-phase wave. Moreover, an innovative method is introduced to solve the model problem associated with the high-genus Riemann surface, leading to the determination of the leading terms, which is also related with the multi-phase Riemann-Theta function. A general discussion on the case of arbitrary \(N\)-genus soliton gas is also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22634 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Genus two KdV soliton gases and their long-time asymptotics Wang, Deng-Shan Zhu, Dinghao Zhu, Xiaodong Exactly Solvable and Integrable Systems Mathematical Physics This paper employs the Riemann-Hilbert problem to provide a comprehensive analysis of the asymptotic behavior of the high-genus Korteweg-de Vries soliton gases. It is demonstrated that the two-genus soliton gas is related to the two-phase Riemann-Theta function as \(x \to +\infty\), and approaches to zero as \(x \to -\infty\). Additionally, the long-time asymptotic behavior of this two-genus soliton gas can be categorized into five distinct regions in the \(x\)-\(t\) plane, which from left to right are rapidly decay, modulated one-phase wave, unmodulated one-phase wave, modulated two-phase wave, and unmodulated two-phase wave. Moreover, an innovative method is introduced to solve the model problem associated with the high-genus Riemann surface, leading to the determination of the leading terms, which is also related with the multi-phase Riemann-Theta function. A general discussion on the case of arbitrary \(N\)-genus soliton gas is also presented. |
| title | Genus two KdV soliton gases and their long-time asymptotics |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2410.22634 |