19 citations · 42 across the 10 of their papers we have counts for
5 papers · 1 filter
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…
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…
Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras
Alexey A. Magazev, Vitaly V. Mikheyev, Igor V. Shirokov
Methods of construction of the composition function, left- and right-invariant vector fields and differential 1-forms of a Lie group from the structure constants of the associated…
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…
Darboux Coordinates on K-Orbits and the Spectra of Casimir Operators on Lie Groups
I. V. Shirokov
We propose an algorithm for obtaining the spectra of Casimir (Laplace) operators on Lie groups. We prove that the existence of the normal polarization associated with a linear func…