Hamiltonian system for the elliptic form of Painleve VI equation

被引：14

作者：

Chen, Zhijie ^{[1
]}

Kuo, Ting-Jung ^{[2
]}

Lin, Chang-Shou ^{[3
]}

机构：

[1] Natl Taiwan Univ, CASTS, Taipei 10617, Taiwan

[2] Natl Taiwan Univ, TIMS, Taipei 10617, Taiwan

[3] Natl Taiwan Univ, CASTS, TIMS, Taipei 10617, Taiwan

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2016年 / 106卷 / 03期

关键词：

Painleve VI equation; The elliptic form; Isomonodromy theory; Hamiltonian system; DIFFERENTIAL-EQUATIONS; HEUN EQUATION; DEFORMATION; MONODROMY; 2ND-ORDER;

D O I：

10.1016/j.matpur.2016.03.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In literature, it is known that any solution of Painleve VI equation governs the isomonodromic deformation of a second order linear Fuchsian ODE on CP1. In this paper, we extend this isomonodromy theory on CP1 to the moduli space of elliptic curves by studying the isomonodromic deformation of the generalized Lame equation. Among other things, we prove that the isomonodromic equation is a new Hamiltonian system, which is equivalent to the elliptic form of Painleve VI equation for generic parameters. For Painleve VI equation with some special parameters, the isomonodromy theory of the generalized Lame equation greatly simplifies the computation of the monodromy group in CP1. This is one of the advantages of the elliptic form. (C) 2016 Elsevier Masson SAS. All rights reserved.

引用

页码：546 / 581

页数：36

共 31 条

[1]

[Anonymous], 1995, Geometry and Analysis (Bombay, 1992

[2]

Babich M. V., 1997, Z251997 NT

[3] Non-canonical extension of θ-functions and modular integrability of θ-constants [J].