Asymptotic symmetries of difference equations on a lattice

TL;DR

This paper extends the concept of asymptotic symmetries, previously used for PDEs, to difference equations on a lattice, providing new insights into their invariant properties.

Contribution

It introduces a method to analyze asymptotic symmetries of difference equations, expanding the framework from PDEs to discrete lattice systems.

Findings

Extended asymptotic symmetry analysis to difference equations.

Identified conditions under which lattice equations exhibit asymptotic invariance.

Provided a new tool for studying solutions of discrete models in mathematical physics.

Abstract

It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In this note we extend the approach to asymptotic symmetries for the analysis of PDEs, to the case of difference equations.