Constructing discrete Painlevé equations: from E8(1) to A1(1) and back

DOI

10.1080/14029251.2019.1640462How to use a DOI?

Keywords

discrete Painlevé equations; affine Weyl groups; restoration method

Abstract

The ‘restoration method’ is a novel method we recently introduced for systematically deriving discrete Painlevé equations. In this method we start from a given Painlevé equation, typically with E8(1) symmetry, obtain its autonomous limit and construct all possible QRT-canonical forms of mappings that are equivalent to it by homographic transformations. Discrete Painlevé equations are then obtained by deautonomising the various mappings thus obtained. We apply the restoration method to two challenging examples, one of which does not lead to a QRT mapping at the autonomous limit but we verify that even in that case our method is indeed still applicable. For one of the equations we derive we also show how, starting from a form where the independent variable advances one step at a time, we can obtain versions that correspond to multiple-step evolutions.

Copyright

© 2019 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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TY  - JOUR
AU  - A. Ramani
AU  - B. Grammaticos
AU  - R. Willox
AU  - T. Tamizhmani
PY  - 2019
DA  - 2019/07/09
TI  - Constructing discrete Painlevé equations: from E8(1) to A1(1) and back
JO  - Journal of Nonlinear Mathematical Physics
SP  - 520
EP  - 535
VL  - 26
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2019.1640462
DO  - 10.1080/14029251.2019.1640462
ID  - Ramani2019
ER  -