Open Access

On the identity of two q-discrete Painlevé equations and their geometrical derivation

Advances in Difference Equations20062006:036397

DOI: 10.1155/ADE/2006/36397

Received: 9 October 2005

Accepted: 5 January 2006

Published: 11 June 2006

Abstract

We show that two recently discovered q-discrete Painlevé equations are one and the same system. Moreover we provide a novel derivation of this q-discrete system based on transformations obtained with the help of affine Weyl groups.

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Authors’ Affiliations

(1)
GMPIB, Université Paris VII
(2)
CPT, Ecole Polytechnique
(3)
Faculty of Marine Technology, Tokyo University of Marine Science and Technology

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Copyright

© B. Grammaticos et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.