Hamiltonian system for the elliptic form of Painlevé VI equation

Zhijie Chen, Ting Jung Kuo, Chang Shou Lin*

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

11 引文 斯高帕斯(Scopus)

摘要

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.

原文英語
頁(從 - 到)546-581
頁數36
期刊Journal des Mathematiques Pures et Appliquees
106
發行號3
DOIs
出版狀態已發佈 - 2016 九月 1
對外發佈

ASJC Scopus subject areas

  • 數學(全部)
  • 應用數學

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