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An Isaac Newton Institute Workshop

Painleve Equations and Monodromy Problems: An Introduction

Symmetry reductions of integrable equations on quad-graphs and discrete Painlev\'e equations

13th September 2006

Author: Tongas, A (University of Patras, Department of Mathematics, Patras, Greece)

Abstract

We investigate the Lie point and generalized symmetries of certain integrable equations on quad-graphs. After introducing symmetry group techniques, we give a number of illustrative examples of discrete Painlev\'e equations arising as group invariant solutions of the relevant integrable lattice equations. The associated isomonodromic deformation problems are constructed through the symmetry reduction as well.