The Boundary Condition for Some Isomonodromy Equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910377008168960 |
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| author | Tang, Qian Xu, Xiaomeng |
| author_facet | Tang, Qian Xu, Xiaomeng |
| contents | In this article, we study a special class of Jimbo-Miwa-Mori-Sato isomonodromy equations, which can be seen as a higher-dimensional generalization of Painlevé VI. We first construct its convergent $n\times n$ matrix series solutions satisfying certain boundary condition. We then use the Riemann-Hilbert approach to prove that the resulting solutions are almost all the solutions. Along the way, we find a shrinking phenomenon of the eigenvalues of the submatrices of the generic matrix solutions in the long time behaviour. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_07269 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Boundary Condition for Some Isomonodromy Equations Tang, Qian Xu, Xiaomeng Classical Analysis and ODEs Mathematical Physics 34M04, 34M40, 34M50, 34M55, 34M56 In this article, we study a special class of Jimbo-Miwa-Mori-Sato isomonodromy equations, which can be seen as a higher-dimensional generalization of Painlevé VI. We first construct its convergent $n\times n$ matrix series solutions satisfying certain boundary condition. We then use the Riemann-Hilbert approach to prove that the resulting solutions are almost all the solutions. Along the way, we find a shrinking phenomenon of the eigenvalues of the submatrices of the generic matrix solutions in the long time behaviour. |
| title | The Boundary Condition for Some Isomonodromy Equations |
| topic | Classical Analysis and ODEs Mathematical Physics 34M04, 34M40, 34M50, 34M55, 34M56 |
| url | https://arxiv.org/abs/2402.07269 |