Lie point symmetries of difference equations and lattices

TL;DR

This paper introduces a method to find Lie point symmetries that act on both difference equations and lattices, aiding in solving differential-difference equations.

Contribution

The paper presents a novel method for identifying Lie point symmetries of difference schemes and lattices, enhancing solution techniques for differential-difference equations.

Findings

Symmetry groups help find particular solutions.

Method applied successfully to multiple examples.

Symmetries preserve the solution set of difference schemes.

Abstract

A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference scheme invariant. The method is applied to several examples. The found symmetry groups are used to obtain particular solutions of differential-difference equations.