Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein–Gordon equations

@article{Boyko2021RealizationsOL,
  title={Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein–Gordon equations},
  author={Vyacheslav M. Boyko and Oleksandra V. Lokaziuk and Roman O. Popovych},
  journal={Analysis and Mathematical Physics},
  year={2021}
}
Essentially generalizing Lie's results, we prove that the contact equivalence groupoid of a class of (1+1)-dimensional generalized nonlinear Klein-Gordon equations is the first-order prolongation of its point equivalence groupoid, and then we carry out the complete group classification of this class. Since it is normalized, the algebraic method of group classification is naturally applied here. Using the specific structure of the equivalence group of the class, we essentially employ the… 
Admissible transformations and Lie symmetries of linear systems of second-order ordinary differential equations
We comprehensively study admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several
Group classification of a family of generalized Klein-Gordon equations by the method of indeterminates
  • J. Ndogmo
  • Mathematics
    Journal of Physics: Conference Series
  • 2021
A method for the group classification of differential equations we recently proposed is applied to the classification of a family of generalized Klein-Gordon equations. Our results are compared with
Lie symmetry structure of nonlinear wave equations
We study Lie point symmetry structure of generalized nonlinear wave equations of the form u = F (x, u,∇u) where is the (n + 1)-dimensional spacetime wave (or d’Alembert) operator, x ∈ Rn+1 (n ≥ 2).

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