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arXiv · 2402.07269

The Boundary Condition for Some Isomonodromy Equations

Qian Tang·Xiaomeng Xu
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Abstract

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 Painlev\'e 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.

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BibTeXRIS

Qian Tang, Xiaomeng Xu. 2024-02-11. The Boundary Condition for Some Isomonodromy Equations. https://arxiv.org/abs/2402.07269

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