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

Zhijie Chen; Ting Jung Kuo; Chang Shou Lin

doi:10.1016/j.geomphys.2017.01.016

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

Zhijie Chen^*, Ting Jung Kuo, Chang Shou Lin

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

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 D_N, where D_N 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 language	English
Pages (from-to)	52-63
Number of pages	12
Journal	Journal of Geometry and Physics
Volume	116
DOIs	https://doi.org/10.1016/j.geomphys.2017.01.016
Publication status	Published - 2017 Jun 1
Externally published	Yes

Keywords

Algebraic solution
Painlevé VI equation
Pole distribution

ASJC Scopus subject areas

Mathematical Physics
General Physics and Astronomy
Geometry and Topology

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10.1016/j.geomphys.2017.01.016

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title = "Unitary monodromy implies the smoothness along the real axis for some Painlev{\'e} VI equation, I",

abstract = "In this paper, we study the Painlev{\'e} 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}.",

keywords = "Algebraic solution, Painlev{\'e} VI equation, Pole distribution",

author = "Zhijie Chen and Kuo, {Ting Jung} and Lin, {Chang Shou}",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2017",

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doi = "10.1016/j.geomphys.2017.01.016",

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TY - JOUR

T1 - Unitary monodromy implies the smoothness along the real axis for some Painlevé VI equation, I

AU - Chen, Zhijie

AU - Kuo, Ting Jung

AU - Lin, Chang Shou

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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}.

AB - 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}.

KW - Algebraic solution

KW - Painlevé VI equation

KW - Pole distribution

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DO - 10.1016/j.geomphys.2017.01.016

M3 - Article

AN - SCOPUS:85011632800

SN - 0393-0440

VL - 116

SP - 52

EP - 63

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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