Advances in Difference Equations
Volume 2006 (2006), Article ID 36397, 11 pages

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

B. Grammaticos,1 A. Ramani,2 and T. Takenawa3

1GMPIB, Université Paris VII, Tour 24-14, 5e étage, Paris 75251, France
2CPT, Ecole Polytechnique, CNRS, UMR 7644, Palaiseau 91128, France
3Faculty of Marine Technology, Tokyo University of Marine Science and Technology, 2-1-6 Etchu-jima, Koto-ku, Tokyo 135-8533, Japan

Received 9 October 2005; Revised 5 January 2006; Accepted 5 January 2006

Copyright © 2006 B. Grammaticos et al. 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.


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.