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

N1 - Publisher Copyright:
© 2017 Elsevier B.V.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

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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U2 - 10.1016/j.geomphys.2017.01.016

DO - 10.1016/j.geomphys.2017.01.016

M3 - Article

AN - SCOPUS:85011632800

VL - 116

SP - 52

EP - 63

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

ER -