Unitary monodromy implies the smoothness along the real axis for some Painlevé VI equation, I

Zhijie Chen, Ting Jung Kuo, Chang Shou Lin

Research output: Contribution to journalArticle

2 Citations (Scopus)


In this paper, we study the Painlevé VI equation with parameter (98,−18, 18, 38). We prove (i) An explicit formula to count the number of poles of an algebraic solution with the monodromy group of the associated linear ODE being DN, where DN is the dihedral group of order 2N. (ii) There are only four solutions without poles in C∖{0,1}. (iii) If the monodromy group of the associated linear ODE of a solution λ(t) is unitary, then λ(t) has no poles in R∖{0,1}.

Original languageEnglish
Pages (from-to)52-63
Number of pages12
JournalJournal of Geometry and Physics
Publication statusPublished - 2017 Jun 1



  • Algebraic solution
  • Painlevé VI equation
  • Pole distribution

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

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