Journal of Nonlinear Mathematical Physics

Volume 20, Issue Supplement 1, November 2013, Pages 3 - 16

Bäcklund transformations for certain rational solutions of Painlevé VI

Authors
Johan van de Leur
Mathematical Institute, University of Utrecht, P.O. Box 80010, 3508 TA Utrecht, The Netherlands, J.W.vandeLeur@uu.nl
Henrik Aratyn
Department of Physics, University of Illinois at Chicago, 845 W. Taylor St., Chicago, IL 60607-7059, aratyn@uic.edu
Received 21 August 2012, Accepted 11 June 2013, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2013.862430How to use a DOI?
Keywords
Painlevéequations, Bäcklund, Grassmannian, KP
Abstract

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 F4(1) root lattice. We thus obtain Bäcklund transformations that relate Painlevé VI tau functions, parametrized by the elements of this F4(1) root lattice.

Copyright
© 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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
20 - Supplement 1
Pages
3 - 16
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2013.862430How to use a DOI?
Copyright
© 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
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  - https://doi.org/10.1080/14029251.2013.862430
ID  - vandeLeur2021
ER  -