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 20 articles , 1 standard article )

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  1. Mohammadi, Zahra; Reid, Gregory J.; Huang, S.-L. Tracy: Symmetry-based algorithms for invertible mappings of polynomially nonlinear PDE to linear PDE (2021)
  2. Chen, Cheng; Jiang, Yao-Lin: Lie group analysis, exact solutions and new conservation laws for combined KdV-mKdV equation (2020)
  3. Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Michels, Dominik L.: On the algorithmic linearizability of nonlinear ordinary differential equations (2020)
  4. Naz, Rehana; Naeem, Imran: Exact solutions of a Black-Scholes model with time-dependent parameters by utilizing potential symmetries (2020)
  5. Mohammadi, Zahra; Reid, Gregory J.; Huang, Tracy Shih-lung: Introduction of the MapDE algorithm for determination of mappings relating differential equations (2019)
  6. Lisle, Ian G.; Huang, S.-L. Tracy: Algorithmic calculus for Lie determining systems (2017)
  7. Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Michels, Dominik L.: Algorithmic verification of linearizability for ordinary differential equations (2017)
  8. de Melo, G. R.; de Montigny, M.; Pinfold, J.; Tuszynski, J. A.: Symmetries and soliton solutions of the Galilean complex Sine-Gordon equation (2016)
  9. Michels, Dominik L.; Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Hossain, Zahid; Riedel-Kruse, Ingmar H.; Weber, Andreas G.: On the general analytical solution of the kinematic Cosserat equations (2016)
  10. Luiz de Souza, Wescley; de Mello Silva, Érica: Time-dependent exact solutions for Rosenau-Hyman equations with variable coefficients (2015)
  11. Chaolu, Temuer; Bluman, G.: An algorithmic method for showing existence of nontrivial non-classical symmetries of partial differential equations without solving determining equations (2014)
  12. Lisle, Ian G.; Huang, S.-L. Tracy; Reid, Greg J.: Structure of symmetry of PDE: exploiting partially integrated systems (2014)
  13. Paliathanasis, Andronikos; Tsamparlis, Michael: The reduction of the Laplace equation in certain Riemannian spaces and the resulting type II hidden symmetries (2014)
  14. Dos Santos Cardoso-Bihlo, Elsa; Popovych, Roman O.: Complete point symmetry group of the barotropic vorticity equation on a rotating sphere (2013)
  15. Tsamparlis, Michael; Paliathanasis, Andronikos: Type II hidden symmetries for the homogeneous heat equation in some general classes of Riemannian spaces (2013)
  16. Naz, Rehana: Conservation laws for some systems of nonlinear partial differential equations via multiplier approach (2012)
  17. Naz, Rehana; Khan, Mohammad Danish; Naeem, Imran: Nonclassical symmetry analysis of boundary layer equations (2012)
  18. Vu, K. T.; Jefferson, G. F.; Carminati, J.: Finding higher symmetries of differential equations using the MAPLE package DESOLVII (2012)
  19. Dos Santos Cardoso-Bihlo, Elsa; Bihlo, Alexander; Popovych, Roman O.: Enhanced preliminary group classification of a class of generalized diffusion equations (2011)
  20. Rocha Filho, Tarcísio M.; Figueiredo, Annibal: [SADE] a Maple package for the symmetry analysis of differential equations (2011)