Volume 24, Issue 4, September 2017, Pages 571 - 583
Note on algebro-geometric solutions to triangular Schlesinger systems
Authors
Vladimir Dragović
Department of Mathematical Sciences, University of Texas at Dallas, 800 West Campbell Road, Richardson TX 75080, USA
Mathematical Institute SANU, Kneza Mihaila 36, Belgrade 11000, Serbia.Vladimir.Dragovic@utdallas.edu
Vasilisa Shramchenko
Department of mathematics, University of Sherbrooke, 2500, boulevard de l’Université, Sherbrooke J1 K 2R1, Quebec, Canada.Vasilisa.Shramchenko@Usherbrooke.ca
Received 22 March 2017, Accepted 16 June 2017, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2017.1375692How to use a DOI?
- Keywords
- Schlesinger systems; hyperelliptic curves; Painlevé equations
- 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
- Copyright
- © 2017 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - JOUR AU - Vladimir Dragović AU - Vasilisa Shramchenko PY - 2021 DA - 2021/01/06 TI - Note on algebro-geometric solutions to triangular Schlesinger systems JO - Journal of Nonlinear Mathematical Physics SP - 571 EP - 583 VL - 24 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2017.1375692 DO - 10.1080/14029251.2017.1375692 ID - Dragović2021 ER -