Journal of Nonlinear Mathematical Physics

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Volume 27, Issue 1, October 2019, Pages 95 - 105

Interrelations of discrete Painlevé equations through limiting procedures

Authors
A. Ramani, B. Grammaticos*
IMNC, CNRS, Université Paris-Diderot, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
T. Tamizhmani
SAS, Vellore Institute of Technology, Vellore - 632014, Tamil Nadu, India
*Corresponding author
Corresponding Author
B. Grammaticos
Received 4 June 2019, Accepted 8 July 2019, Available Online 25 October 2019.
DOI
10.1080/14029251.2020.1683981How to use a DOI?
Keywords
discrete Painlevé equations; affine Weyl groups; limiting procedures; canonical forms
Abstract

We study the discrete Painlevé equations associated to the E7(1) affine Weyl group which can be obtained by the implementation of a special limits of E8(1)-associated equations. This study is motivated by the existence of two E7(1)-associated discrete both having a double ternary dependence in their coefficients and which have not been related before. We show here that two equations correspond to two different limits of a E8(1)-associated discrete Painlevé equation. Applying the same limiting procedures to other E8(1)-associated equations we obtained several E7(1)-related equations most of which have not been previously derived.

Copyright
© 2020 The Authors. Published by Atlantis 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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<Previous Article In Issue
Next Article In Issue>
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 1
Pages
95 - 105
Publication Date
2019/10/25
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1683981How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis 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

risenwbib
TY  - JOUR
AU  - A. Ramani
AU  - B. Grammaticos
AU  - T. Tamizhmani
PY  - 2019
DA  - 2019/10/25
TI  - Interrelations of discrete Painlevé equations through limiting procedures
JO  - Journal of Nonlinear Mathematical Physics
SP  - 95
EP  - 105
VL  - 27
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1683981
DO  - 10.1080/14029251.2020.1683981
ID  - Ramani2019
ER  -