Symmetries and Reduction of Discrete Painleve Equations

TL;DR

This paper analyzes the symmetries of discrete Painleve equations, using them to find exact solutions, and enhances understanding of their structure and solution methods.

Contribution

It provides a symmetry analysis framework for discrete Painleve equations assuming characteristics depend only on n and u_n, leading to new exact solutions.

Findings

Identified symmetries for discrete Painleve equations

Constructed exact solutions using symmetry methods

Enhanced understanding of the structure of discrete Painleve equations

Abstract

The construction and role of symmetries for difference equations are now well known. In this paper, the symmetry analysis of the discrete Painleve equations is considered. We assume that the characteristics depend on $n$ and $u_n$ only and we obtain a number of symmetries. These symmetries are used to construct exact solutions in some cases.