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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

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


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.


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

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Authors’ Affiliations

GMPIB, Université Paris VII, Tour 24-14, 5e étage, Paris, 75251, France
CPT, Ecole Polytechnique, CNRS, UMR 7644, Palaiseau, 91128, France
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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© 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.