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 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 language | English |
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Pages (from-to) | 52-63 |
Number of pages | 12 |
Journal | Journal of Geometry and Physics |
Volume | 116 |
DOIs | |
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