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:

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  1. Kumar, Sachin; Jyoti, Divya: Generalised two-component modified weakly dissipative Dullin-Gottwald-Holm system: invariance analysis and conservation laws (2022)
  2. Gupta, R. K.; Kaur, Bikramjeet: On symmetries and conservation laws of Einstein-Maxwell equations for non-static cylindrical symmetric metric (2021)
  3. Mohammadi, Zahra; Reid, Gregory J.; Huang, S.-L. Tracy: Symmetry-based algorithms for invertible mappings of polynomially nonlinear PDE to linear PDE (2021)
  4. Moitsheki, Raseelo J.; Ntsime, Basetsana P.: Potential symmetry reduction of a convection-dispersion equation with spatial dependent water velocity (2021)
  5. Cheviakov, A. F.; Dorodnitsyn, V. A.; Kaptsov, E. I.: Invariant conservation law-preserving discretizations of linear and nonlinear wave equations (2020)
  6. Freire, Igor Leite; Filho, Nazime Sales; de Souza, Ligia Corrêa; Toffoli, Carlos Eduardo: Invariants and wave breaking analysis of a Camassa-Holm type equation with quadratic and cubic non-linearities (2020)
  7. Gün Polat, Gülden; Özer, Teoman: On group analysis of optimal control problems in economic growth models (2020)
  8. Gün Polat, Gülden; Özer, Teoman: The group-theoretical analysis of nonlinear optimal control problems with Hamiltonian formalism (2020)
  9. Jamal, Sameerah: New multipliers of the barotropic vorticity equations (2020)
  10. Naz, Rehana; Naeem, Imran: Exact solutions of a Black-Scholes model with time-dependent parameters by utilizing potential symmetries (2020)
  11. Opanasenko, Stanislav; Popovych, Roman O.: Generalized symmetries and conservation laws of (1 + 1)-dimensional Klein-Gordon equation (2020)
  12. Popovych, Roman O.; Bihlo, Alexander: Inverse problem on conservation laws (2020)
  13. Sil, Subhankar; Raja Sekhar, T.; Zeidan, Dia: Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation (2020)
  14. Sun, Xiaoqian; Yong, Xuelin; Gao, Jianwei: Optimal portfolio for a defined-contribution pension plan under a constant elasticity of variance model with exponential utility (2020)
  15. Zhao, Peng; Fan, Engui: Finite gap integration of the derivative nonlinear Schrödinger equation: a Riemann-Hilbert method (2020)
  16. Bai, Tonglaga; Chaolu, Temuer: A potential constraints method of finding nonclassical symmetry of PDEs based on Wu’s method (2019)
  17. Feng, Wei: On symmetry groups and conservation laws for space-time fractional inhomogeneous nonlinear diffusion equation (2019)
  18. Giresunlu, İlker Burak; Yaşar, Emrullah; Rashid Adem, Abdullahi: The logarithmic ((1+1))-dimensional KdV-like and ((2+1))-dimensional KP-like equations: Lie group analysis, conservation laws and double reductions (2019)
  19. Heß, Julian; Cheviakov, Alexei F.: A solution set-based entropy principle for constitutive modeling in mechanics (2019)
  20. Manganaro, N.: Conservation laws for (2 \times2) hyperbolic systems (2019)

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