Journal of Nonlinear Mathematical Physics

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
https://doi.org/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 (9n2+12n+48,-n28,n28,4-n28) .

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.

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
24 - 4
Pages
571 - 583
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2017.1375692How to use a DOI?
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
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  - https://doi.org/10.1080/14029251.2017.1375692
ID  - Dragović2021
ER  -