Volume 20, Issue Supplement 1, November 2013, Pages 3 - 16
Bäcklund transformations for certain rational solutions of Painlevé VI
Johan van de Leur
Mathematical Institute, University of Utrecht, P.O. Box 80010, 3508 TA Utrecht, The Netherlands,J.W.vandeLeur@uu.nl
Department of Physics, University of Illinois at Chicago, 845 W. Taylor St., Chicago, IL 60607-7059,email@example.com
Received 21 August 2012, Accepted 11 June 2013, Available Online 6 January 2021.
- 10.1080/14029251.2013.862430How to use a DOI?
- Painlevéequations; Bäcklund; Grassmannian; KP
We introduce certain Bäcklund transformations for rational solutions of the Painlevé VI equation. These transformations act on a family of Painlevé VI tau functions. They are obtained from reducing the Hirota bilinear equations that describe the relation between certain points in the 3 component polynomial KP Grassmannian. In this way we obtain transformations that act on the root lattice of A5. We also show that this A5 root lattice can be related to the root lattice. We thus obtain Bäcklund transformations that relate Painlevé VI tau functions, parametrized by the elements of this root lattice.
- © 2013 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Johan van de Leur AU - Henrik Aratyn PY - 2021 DA - 2021/01/06 TI - Bäcklund transformations for certain rational solutions of Painlevé VI JO - Journal of Nonlinear Mathematical Physics SP - 3 EP - 16 VL - 20 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2013.862430 DO - 10.1080/14029251.2013.862430 ID - vandeLeur2021 ER -