# Symmetry Analysis and Conservation Laws of some third-order Difference Equations

## TL;DR

This paper presents a method to find Lie symmetries of third-order difference equations, enabling order reduction and solution derivation, along with a technique for obtaining their first integrals.

## Contribution

It introduces a new approach for symmetry analysis and solution methods specifically for third-order difference equations.

## Key findings

- Lie symmetries can be systematically found for third-order difference equations.
- Symmetries facilitate order reduction and solution derivation.
- A technique for obtaining first integrals of these equations is proposed.

## Abstract

We derive a method for finding Lie Symmetries for third-order difference equations. We use these symmetries to reduce the order of the difference equations and hence obtain the solutions of some third-order difference equations. We also introduce a technique for obtaining their first integrals.