Invariance analysis, reductions and conservation laws for second-order systems of ordinary difference equations

TL;DR

This paper introduces methods to identify symmetries and conservation laws in second-order systems of ordinary difference equations, enabling order reduction and deeper understanding of their structure.

Contribution

It presents novel techniques for symmetry detection and conservation law discovery specifically tailored for second-order difference systems.

Findings

Symmetry-based order reduction demonstrated.

New conservation law finding method introduced.

Applicable to various second-order difference systems.

Abstract

We present a method to obtain symmetries for second-order systems of ordinary difference equations and how to use them to reduce the order. We also introduce a technique of finding conservation laws for such systems.