<Previous Article In Issue
Volume 23, Issue 1, January 2016, Pages 141 - 149
Parameterless discrete Painlevé equations and their Miura relations
Authors
B. Grammaticos
IMNC, Université Paris VII & XI, CNRS, UMR 8165, Bât. 440. 91406 Orsay, France,grammaticos@imnc.in2p3.fr
A. Ramani
Centre de Physique Théorique, Ecole Polytechnique CNRS, Université Paris-Saclay, 91128 Palaiseau, France,Alfred.Ramani@cpht.polytechnique.fr
Received 21 October 2015, Accepted 1 December 2015, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2016.1135647How to use a DOI?
- Keywords
- discrete Painlevé equations; Miura transformations; continuous limits
- Abstract
We present a study of discrete Painlevé equations which do not have any parameter, apart from those that can be removed by the appropriate scaling. We find four basic equations of this type as well as several more related to the basic ones by Miura transformations, which we derive explicitly. We obtain also the continuous limits of the basic parameterless equations and show that two of them are the discrete analogues of both the continuous Painlevé I and the zero-parameter Painlevé III.
- Copyright
- © 2016 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/).
<Previous Article In Issue
Cite this article
TY - JOUR AU - B. Grammaticos AU - A. Ramani PY - 2021 DA - 2021/01/06 TI - Parameterless discrete Painlevé equations and their Miura relations JO - Journal of Nonlinear Mathematical Physics SP - 141 EP - 149 VL - 23 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2016.1135647 DO - 10.1080/14029251.2016.1135647 ID - Grammaticos2021 ER -