|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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