50 citations · 70 across the 16 of their papers we have counts for
7 papers · 1 filter
An Operator Approach to the Integration of Linear Differential Equations
O. V. Kaptsov
We develop an operator approach to the integration of linear differential equations based on intertwining relations between differential operators. Conditions for the existence of…
General solutions to the equations of acoustics in inhomogeneous media and gas dynamics
O. V. Kaptsov
This paper considers one-dimensional equations of acoustics equations of inhomogeneous media and the system of gas dynamics equations with constant entropy. Using the Riemann appro…
Representation of Linear Waves in Inhomogeneous Media
O. V. Kaptsov
The article explores the acoustic equations in inhomogeneous media and the linearized shallow water equations. Two methods for integrating these equations are proposed. The first m…
Application of invariants of characteristics to construction of solutions without gradient catastrophe
Alexander V. Aksenov, Konstantin P. Druzhkov, Oleg V. Kaptsov
The one-dimensional system of equations of isentropic gas dynamics is considered. First-order invariants of characteristics of this system are classified. Second-order invariants o…
Application of the B-Determining Equations Method to One Problem of Free Turbulence
Oleg V. Kaptsov, Alexey V. Schmidt
A three-dimensional model of the far turbulent wake behind a self-propelled body in a passively stratified medium is considered. The model is reduced to a system of ordinary differ…
Linear determining equations, differential constraints and invariant solutions
O. V. Kaptsov, A. V. Schmidt
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such…