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arXiv · 2512.19381

Asymptotic and monodromy problems for higher-order Painlev\'e III equations

Zikang Wang·Xiaomeng Xu
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Abstract

In this paper, we study the isomonodromy deformation equations for the $n\times n$ system of first order meromorphic linear ordinary differential equations with two second order poles. We analyze the asymptotic behaviour of the solutions at a boundary point of the isomonodromic deformation space, and derive a parameterization of the solutions via asymptotic parameters. We then derive the explicit formula for the Stokes matrices and connection matrix of the associated linear system in terms of the asymptotic parameters. In the end, we apply the results to the study of the $tt^{*}$ equations.

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Zikang Wang, Xiaomeng Xu. 2025-12-22. Asymptotic and monodromy problems for higher-order Painlev\'e III equations. https://arxiv.org/abs/2512.19381

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