4 papers
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…
Integration of geodesic flows on homogeneous spaces: the case of a wild lie group
A. A. Magazev, I. V. Shirokov
We obtain necessary and sufficient conditions for the integrability in quadratures of geodesic flows on homogeneous spaces with invariant and central metrics. The proposed inte…