5 papers
Inverse construction of exact atmospheric models and the 3.7--4.4\,mHz acoustic resonances
O. V. Kaptsov
Large explosive eruptions and earthquakes excite atmospheric oscillations near 3.7 and 4.4\,mHz that couple to the solid Earth. For vertically propagating linear acoustic--gravity…
Exact Harmonic Dimensional Reduction and Conformal Lifting for Multicomponent Nonlinear Schrödinger Systems
O. V. Kaptsov
A harmonic dimensional reduction framework is developed for systems of coupled nonlinear Schrödinger-type equations with stationary transverse trapping potentials…
Solutions of Three-Dimensional Stationary Gas Dynamics Equations
O. V. Kaptsov
This paper examines the three-dimensional stationary equations of a polytropic gas and employs symmetry methods to construct exact analytical solutions. In the Chaplygin gas case,…
Exponential map of germs of vector fields
Oleg Kaptsov
In this paper we introduce an exponential map of the algebra of germs of vector fields into the group of germs of diffeomorphisms at zero. It is shown that this mapping is not a bi…
Symmetries of linear and nonlinear partial differential equations
Oleg Kaptsov
We consider higher symmetries and operator symmetries of linear partial differential equations. The higher symmetries form a Lie algebra, and operator ones form an associative alge…