50 citations · 70 across the 16 of their papers we have counts for
16 papers
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…
Contact germs and partial differential equations
O. V. Kaptsov
The article introduces contact germs that transform solutions of some partial differential equations into solutions of other equations. Parametric symmetries of differential equati…
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…
Solutions of the Euler equations and stationary structures in an inviscid fluid
O. V. Kaptsov
The Euler equations describing two-dimensional steady flows of an inviscid fluid are studied. These equations are reduced to one equation for the stream function and then, using th…