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  • Research Article
  • Open Access

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

Advances in Difference Equations20062006:036397

https://doi.org/10.1155/ADE/2006/36397

  • Received: 9 October 2005
  • Accepted: 5 January 2006
  • Published:

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.

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation

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Authors’ Affiliations

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

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