Hamiltonian system for the elliptic form of Painlevé VI equation

Zhijie Chen, Ting Jung Kuo, Chang Shou Lin

研究成果: Article査読

11 被引用数 (Scopus)

抄録

In literature, it is known that any solution of Painlevé 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 Lamé equation. Among other things, we prove that the isomonodromic equation is a new Hamiltonian system, which is equivalent to the elliptic form of Painlevé VI equation for generic parameters. For Painlevé VI equation with some special parameters, the isomonodromy theory of the generalized Lamé equation greatly simplifies the computation of the monodromy group in CP1. This is one of the advantages of the elliptic form.

本文言語English
ページ(範囲)546-581
ページ数36
ジャーナルJournal des Mathematiques Pures et Appliquees
106
3
DOI
出版ステータスPublished - 2016 9 1
外部発表はい

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

フィンガープリント 「Hamiltonian system for the elliptic form of Painlevé VI equation」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル