Moduli Spaces for the Fifth Painlevé Equation

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-09-26 DOI:10.3842/sigma.2023.068

Marius van der Put, Jaap Top

引用次数: 0

Abstract

Isomonodromy for the fifth Painlevé equation ${\rm P}_5$ is studied in detail in the context of certain moduli spaces for connections, monodromy, the Riemann-Hilbert morphism, and Okamoto-Painlevé spaces. This involves explicit formulas for Stokes matrices and parabolic structures. The rank 4 Lax pair for ${\rm P}_5$, introduced by Noumi-Yamada et al., is shown to be induced by a natural fine moduli space of connections of rank 4. As a by-product one obtains a polynomial Hamiltonian for ${\rm P}_5$, equivalent to the one of Okamoto.

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第五阶painlevleve方程的模空间

在连接模空间、单态、Riemann-Hilbert态射和okamoto - painlev空间的背景下，详细研究了第五阶painlev方程${\rm P}_5$的等同构性。这涉及Stokes矩阵和抛物结构的显式公式。由Noumi-Yamada等人引入的${\rm P}_5$的4阶Lax对被证明是由4阶连接的自然精细模空间诱导出来的。作为副产物，我们得到${\rm P}_5$的多项式哈密顿量，等价于冈本的哈密顿量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.