21 citations · 48 across the 8 of their papers we have counts for
8 papers
Pseudo-Riemannian Lie algebras with coisotropic ideals and integrating the Laplace-Beltrami equation on Lie groups
A. A. Magazev, I. V. Shirokov
We identify a class of left-invariant pseudo-Riemannian metrics on Lie groups for which the Laplace-Beltrami equation reduces to a first-order PDE and admits exact solutions. The d…
Exact solutions of the Klein-Gordon equation in external electromagnetic fields on 3D de Sitter background
Alexey A. Magazev, Maria N. Boldyreva
In this study, we investigate the symmetry properties and the possibility of exact integration of the Klein--Gordon equation in the presence of an external electromagnetic field on…
Classification of scalar second-order differential equations with low-dimensional symmetry groups: The case of free action
Alexey A. Magazev, Igor V. Shirokov
Based on an original classification of differential equations by types of regular Lie group actions, we offer a systematic procedure for describing partial differential equations w…
Constructing a complete integral of the Hamilton-Jacobi equation on pseudo-Riemannian spaces with simply transitive groups of motions
A. A. Magazev
In this work, an efficient method for constructing a complete integral of the geodesic Hamilton-Jacobi equation on pseudo-Riemannian manifolds with simply transitive groups of moti…
A method of integration for classical and quantum equations based on the connection between canonical transformations and irreducible representations of Lie groups
Alexey A. Magazev, Igor V. Shirokov
We propose a method for integrating the right-invariant geodesic flows on Lie groups based on the use of a special canonical transformation in the cotangent bundle of the group. We…
Integrating Klein-Gordon-Fock equations in an external electromagnetic field on Lie groups
Alexey A. Magazev
We investigate the structure of the Klein-Gordon-Fock equation symmetry algebra on pseudo-Riemannian manifolds with motions in the presence of an external electromagnetic field. We…