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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