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 75 articles , 1 standard article )

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  1. Polat, Gülden Gün; Özer, Teoman: The group-theoretical analysis of nonlinear optimal control problems with Hamiltonian formalism (2020)
  2. Manganaro, N.: Conservation laws for (2 \times2) hyperbolic systems (2019)
  3. Peng, Linyu; Zhang, Zhenning: Statistical Einstein manifolds of exponential families with group-invariant potential functions (2019)
  4. Vaneeva, Olena; Boyko, Vyacheslav; Zhalij, Alexander; Sophocleous, Christodoulos: Classification of reduction operators and exact solutions of variable coefficient Newell-Whitehead-Segel equations (2019)
  5. Wang, Guo; Yong, Xuelin; Huang, Yehui; Tian, Jing: Symmetry, pulson solution, and conservation laws of the Holm-Hone equation (2019)
  6. Zhao, Zhonglong: Conservation laws and nonlocally related systems of the Hunter-Saxton equation for liquid crystal (2019)
  7. Adem, Abdullahi Rashid: On the solutions and conservation laws of a two-dimensional Korteweg de Vries model: multiple (\exp)-function method (2018)
  8. Cheviakov, A. F.; Heß, J.: A symbolic computation framework for constitutive modelling based on entropy principles (2018)
  9. Cheviakov, Alexei F.: Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model (2018)
  10. Kara, Abdul H.: On the relationship between the invariance and conservation laws of differential equations (2018)
  11. Mitsotakis, Dimitrios; Dutykh, Denys; Li, Qian: Asymptotic nonlinear and dispersive pulsatile flow in elastic vessels with cylindrical symmetry (2018)
  12. Sadeghi, H.; Oberlack, M.; Gauding, M.: On new scaling laws in a temporally evolving turbulent plane jet using Lie symmetry analysis and direct numerical simulation (2018)
  13. Satapathy, Purnima; Raja Sekhar, T.: Nonlocal symmetries classifications and exact solution of Chaplygin gas equations (2018)
  14. Yıldırım, Yakup; Yaşar, Emrullah: A (2+1)-dimensional breaking soliton equation: solutions and conservation laws (2018)
  15. Cheviakov, A. F.; Naz, R.: A recursion formula for the construction of local conservation laws of differential equations (2017)
  16. Cheviakov, Alexei F.: Symbolic computation of equivalence transformations and parameter reduction for nonlinear physical models (2017)
  17. 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)
  18. Kontogiorgis, Stavros; Sophocleous, Christodoulos: On the simplification of the form of Lie transformation groups admitted by systems of evolution differential equations (2017)
  19. Lisle, Ian G.; Huang, S.-L. Tracy: Algorithmic calculus for Lie determining systems (2017)
  20. Mhlanga, Isaiah Elvis; Khalique, Chaudry Masood: A study of a generalized Benney-Luke equation with time-dependent coefficients (2017)

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