GeM

We present a recently developed Maple-based “GeM” software package for automated symmetry and conservation law analysis of systems of partial and ordinary differential equations (DE). The package contains a collection of powerful easy-to-use routines for mathematicians and applied researchers. A standard program that employs “GeM” routines for symmetry, adjoint symmetry or conservation law analysis of any given DE system occupies several lines of Maple code, and produces output in the canonical form. Classification of symmetries and conservation laws with respect to constitutive functions and parameters present in the given DE system is implemented. The “GeM” package is being successfully used in ongoing research. Run examples include classical and new results. (Source: http://cpc.cs.qub.ac.uk/summaries/)


References in zbMATH (referenced in 53 articles , 1 standard article )

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  1. Cheviakov, A.F.; Naz, R.: A recursion formula for the construction of local conservation laws of differential equations (2017)
  2. Dierkes, Dominik; Oberlack, Martin: Euler and Navier-Stokes equations in a new time-dependent helically symmetric system: derivation of the fundamental system and new conservation laws (2017)
  3. Kontogiorgis, Stavros; Sophocleous, Christodoulos: On the simplification of the form of Lie transformation groups admitted by systems of evolution differential equations (2017)
  4. Lisle, Ian G.; Huang, S.-L.Tracy: Algorithmic calculus for Lie determining systems (2017)
  5. Buhe, Eerdun; Bluman, G.; Kara, A.H.: Conservation laws for some systems of nonlinear PDEs via the symmetry/adjoint symmetry pair method (2016)
  6. Morris, R.M.; Kara, A.H.; Biswas, Anjan: An analysis of the Zhiber-Shabat equation including Lie point symmetries and conservation laws (2016)
  7. Recio, E.; Gandarias, M.L.; Bruzón, M.S.: Symmetries and conservation laws for a sixth-order Boussinesq equation (2016)
  8. Bruzón, María S.; Gandarias, María L.; Recio, Elena; Anco, Stephen C.: A nonlinear generalization of the Camassa-Holm equation with peakon solutions (2015)
  9. Buhe, Eerdun; Bluman, George W.: Symmetry reductions, exact solutions, and conservation laws of the generalized Zakharov equations (2015)
  10. Cheviakov, A.F.; St.Jean, S.: A comparison of conservation law construction approaches for the two-dimensional incompressible Mooney-Rivlin hyperelasticity model (2015)
  11. Nold, Andreas; Oberlack, Martin; Cheviakov, Alexei F.: On new stability modes of plane canonical shear flows using symmetry classification (2015)
  12. San, Sait; Yaşar, Emrullah: On the conservation laws of Derrida-Lebowitz-Speer-Spohn equation (2015)
  13. Vaneeva, Olena; Kuriksha, Oksana; Sophocleous, Christodoulos: Enhanced group classification of gardner equations with time-dependent coefficients (2015)
  14. Chaolu, Temuer; Bluman, G.: An algorithmic method for showing existence of nontrivial non-classical symmetries of partial differential equations without solving determining equations (2014)
  15. Cheviakov, Alexei F.: Conservation properties and potential systems of vorticity-type equations (2014)
  16. Cheviakov, Alexei F.: Symbolic computation of nonlocal symmetries and nonlocal conservation laws of partial differential equations using the GeM package for Maple (2014)
  17. Ganghoffer, Jean-François (ed.); Mladenov, Ivaïlo (ed.): Similarity and symmetry methods. Applications in elasticity and mechanics of materials. Lecture notes given at the EUROMECH workshop `Similarity, symmetry and group theoretical methods in mechanics, Varna, Bulgaria, June 6--9, 2013 (2014)
  18. Lisle, Ian G.; Huang, S.-L.Tracy; Reid, Greg J.: Structure of symmetry of PDE: exploiting partially integrated systems (2014)
  19. Osman, E.; Khalfallah, M.; Sapoor, H.: Conservation laws for a Degasperis Procesi equation and a coupled variable-coefficient modified Korteweg-de Vries system in a two-layer fluid model via the multiplier approach (2014)
  20. Yang, Zhengzheng; Cheviakov, Alexei F.: Some relations between symmetries of nonlocally related systems (2014)

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