2-Parameter τ-Function for the First Painleve Equation: Topological Recursion and Direct Monodromy Problem via Exact WKB Analysis

被引：0

作者：

Iwaki, Kohei ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, 3-8-1 Komaba, Tokyo 1538914, Japan

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2020年 / 377卷 / 02期

关键词：

ORDINARY DIFFERENTIAL-EQUATIONS; POLYNOMIAL HAMILTONIANS; QUANTUM CURVES; MATRIX MODELS; TRANSCENDENTS; RESURGENCE; DEFORMATION; 2ND-ORDER; PARAMETER; SYSTEMS;

D O I：

10.1007/s00220-020-03769-2

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We show that a 2-parameter family of tau-functions for the first Painleve equation can be constructed by the discrete Fourier transform of the topological recursion partition function for a family of elliptic curves. We also perform an exact WKB theoretic computation of the Stokes multipliers of associated isomonodromy system assuming certain conjectures.

引用

页码：1047 / 1098

页数：52

共 6 条

[1] 2-Parameter τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}-Function for the First Painlevé Equation: Topological Recursion and Direct Monodromy Problem via Exact WKB Analysis
Kohei Iwaki
Communications in Mathematical Physics, 2020, 377 (2) : 1047 - 1098
[2] WKB analysis of painleve transcendents with a large parameter III. Local reduction of 2-parameter Painleve transcendents
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[3] Painlevé 2 Equation with Arbitrary Monodromy Parameter, Topological Recursion and Determinantal Formulas
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[4] Painlev, 2 Equation with Arbitrary Monodromy Parameter, Topological Recursion and Determinantal Formulas
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ANNALES HENRI POINCARE, 2017, 18 (08): : 2581 - 2620
[5] A relation between the exact WKB analysis and the topological recursion - in the case of the Gauss hypergeometric differential equation
Takei, Yumiko
COMPLEX DIFFERENTIAL AND DIFFERENCE EQUATIONS, 2019, : 259 - 266
[6] WKB Analysis of Higher Order Painleve Equations with a Large Parameter. II. Structure Theorem for Instanton-Type Solutions of (PJ)m (J = I, 34, II-2 or IV) near a Simple P-turning Point of the First Kind
Kawai, Takahiro
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PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2011, 47 (01) : 153 - 219

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