Advances in Difference Equations
Volume 2006 (2006), Article ID 36397, 11 pages
doi:10.1155/ADE/2006/36397
On the identity of two q-discrete Painlevé equations and their geometrical derivation
B. Grammaticos1
, A. Ramani2
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
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.