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, order and dimension reductions using Lie symmetries, classification of differential equations, Casimir invariants, and the quasi-polynomial formalism for ODE’s (previously implemented by the authors in the package QPSI) for the determination of quasi-polynomial first-integrals, Lie symmetries and invariant surfaces. Examples of use of the package are given.

References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Lisle, Ian G.; Huang, S.-L.Tracy: Algorithmic calculus for Lie determining systems (2017)
  2. Luiz de Souza, Wescley; de Mello Silva, Érica: Time-dependent exact solutions for Rosenau-Hyman equations with variable coefficients (2015)
  3. Chaolu, Temuer; Bluman, G.: An algorithmic method for showing existence of nontrivial non-classical symmetries of partial differential equations without solving determining equations (2014)
  4. Lisle, Ian G.; Huang, S.-L.Tracy; Reid, Greg J.: Structure of symmetry of PDE: exploiting partially integrated systems (2014)
  5. Paliathanasis, Andronikos; Tsamparlis, Michael: The reduction of the Laplace equation in certain Riemannian spaces and the resulting type II hidden symmetries (2014)
  6. Dos Santos Cardoso-Bihlo, Elsa; Popovych, Roman O.: Complete point symmetry group of the barotropic vorticity equation on a rotating sphere (2013)
  7. Tsamparlis, Michael; Paliathanasis, Andronikos: Type II hidden symmetries for the homogeneous heat equation in some general classes of Riemannian spaces (2013)
  8. Naz, Rehana: Conservation laws for some systems of nonlinear partial differential equations via multiplier approach (2012)
  9. Naz, Rehana; Khan, Mohammad Danish; Naeem, Imran: Nonclassical symmetry analysis of boundary layer equations (2012)
  10. Vu, K.T.; Jefferson, G.F.; Carminati, J.: Finding higher symmetries of differential equations using the MAPLE package DESOLVII (2012)
  11. Dos Santos Cardoso-Bihlo, Elsa; Bihlo, Alexander; Popovych, Roman O.: Enhanced preliminary group classification of a class of generalized diffusion equations (2011)
  12. Rocha Filho, Tarcísio M.; Figueiredo, Annibal: [SADE] a Maple package for the symmetry analysis of differential equations (2011)