New Expressions for Discrete Painlevé Equations

2003/04/01 by Mikio Murata, Murata, Mikio
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0304001

14 pages

arxiv created 2003/06/09 · arxiv updated 2009/11/30

Abstract

It is known that discrete Painlevé equations have symmetries of the affine Weyl groups. In this paper we propose a new representation of discrete Painlevé equations in which the symmetries become clearly visible. We know how to obtain discrete Painlevé equations from certain rational surfaces in connection with the extended affine Weyl groups. By means of this representation, we clarify the relation between the equation and the surface.

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