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

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-Bäcklund and potential symmetries, invariant solutions, first-integrals, Nöther 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.

Cited by in corpus (12)

• Enhanced preliminary group classification of a class of generalized diffusion equations
• The geometric origin of Lie point symmetries of the Schrödinger and the Klein Gordon equations
• Complete point symmetry group of the barotropic vorticity equation on a rotating sphere
• Point symmetry group of the barotropic vorticity equation
• The reduction of Laplace equation in certain Riemannian spaces and the resulting Type II hidden symmetries
• Lie Symmetries of Non-Relativistic and Relativistic Motions
• Hierarchy of coupled Burgers-like equations induced by conditional symmetries
• Type II hidden symmetries for the homogeneous heat equation in some general classes of Riemannian spaces
• On the General Analytical Solution of the Kinematic Cosserat Equations
• Algorithmic Verification of Linearizability for Ordinary Differential Equations
• Option Pricing with Lie Symmetry Analysis and Similarity Reduction Method
• Extensions of the MapDE algorithm for mappings relating differential equations