Interrelations of discrete Painlevé equations through limiting procedures

Abstract

We study the discrete Painlevé equations associated to the affine Weyl group which can be obtained by the implementation of a special limits of -associated equations. This study is motivated by the existence of two -associated discrete both having a double ternary dependence in their coefficients and which have not been related before. We show here that two equations correspond to two different limits of a -associated discrete Painlevé equation. Applying the same limiting procedures to other -associated equations we obtained several -related equations most of which have not been previously derived.

Keywords:

• discrete Painlevé equations
• affine Weyl groups
• limiting procedures
• canonical forms

PACS numbers:

• 02.30.Ik
• 05.45.Yv