Authors: Dragović, Vladimir 
Shramchenko, Vasilisa
Title: Note on algebro-geometric solutions to triangular Schlesinger systems
Journal: Journal of Nonlinear Mathematical Physics
Volume: 24
Issue: 4
First page: 571
Last page: 583
Issue Date: 2-Oct-2017
Rank: M21
ISSN: 1402-9251
DOI: 10.1080/14029251.2017.1375692
Abstract: 
We construct algebro-geometric upper triangular solutions of rank two Schlesinger systems. Using these solutions we derive two families of solutions to the sixth Painlevé equation with parameters (1/8, ‒1/8, 1/8, 3=8) expressed in simple forms using periods of differentials on elliptic curves. Similarly for every integer n different from 0 and ‒1 we obtain one family of solutions to the sixth Painlevé equation with parameters (Figure presented.).
Keywords: hyperelliptic curves | Painlevé equations | Schlesinger systems
Publisher: Taylor & Francis
Project: Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems 
NSF, Grant 1444147

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