Asymptotic and monodromy problems for higher-order Painlevé III equations

2025/12/22 by Zikang Wang, Xiaomeng Xu, Wang, Zikang +1
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Waves and Solitons

paper · doi:10.48550/arxiv.2512.19381

openalex publication_date 2025/12/22 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the isomonodromy deformation equations for the n× 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.

Citations

• WKB asymptotics of Stokes matrices, spectral curves and rhombus inequalities
• The Boundary Condition for Some Isomonodromy Equations
• The tt*-Toda equations of A_n type
• Regularized limits of Stokes matrices, isomonodromy deformation and crystal basis
• Isomonodromy aspects of the tt* equations of Cecotti and Vafa II. Riemann-Hilbert problem
• Isomonodromy aspects of the tt* equations of Cecotti and Vafa I. Stokes data
• Geometry of 2d topological field theories

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• The Degenerate Third Painleve' Equation: Complete Asymptotic Classification of Solutions in the Neighbourhood of the Regular Singular Point