[SADE] A Maple package for the Symmetry Analysis of Differential Equations

TL;DR

SADE is a comprehensive Maple package that automates symmetry analysis of differential equations, including Lie, nonclassical, and potential symmetries, aiding in solving and classifying these equations.

Contribution

The paper introduces SADE, a new Maple package that integrates multiple symmetry analysis methods for differential equations, enhancing computational efficiency and scope.

Findings

Successfully computes various symmetries and invariants.

Facilitates reduction and classification of differential equations.

Includes practical examples demonstrating its capabilities.

Abstract

We present the package SADE (Symmetry Analysis of Differential Equations) for the determination of symmetries and related properties of systems of differential equations. The main methods implemented are: Lie, nonclassical, Lie-B\"acklund and potential symmetries, invariant solutions, first-integrals, N\"other theorem for both discrete and continuous systems, solution of ordinary differential equations, reduction of order or dimension using Lie symmetries, classification of differential equations, Casimir invariants, and the quasi-polynomial formalism for ODE's (previously implemented in the package QPSI by the authors) for the determination of quasi-polynomial first-integrals, Lie symmetries and invariant surfaces. Examples of use of the package are given.