20 citations · 73 across the 7 of their papers we have counts for
6 papers
Exact solutions and automorphic systems of the geopotential forecast equation
E. I. Kaptsov
The study of the recently constructed group foliation for the geopotential forecast equation is continued. The group foliation consists of two systems, namely the automorphic and r…
Group foliations, invariant solutions, and conservation laws of the geopotential forecast equation
E. I. Kaptsov
Despite the large number of publications on symmetry analysis of the geopotential forecast equation, its group foliations laws have not been considered previously. The present publ…
Invariant finite-difference schemes with conservation laws preservation for one-dimensional MHD equations
E. I. Kaptsov, V. A. Dorodnitsyn
Invariant finite-difference schemes are considered for one-dimensional magnetohydrodynamics (MHD) equations in mass Lagrangian coordinates for the cases of finite and infinite cond…
Plane one-dimensional MHD flows: symmetries and conservation laws
Vladimir A. Dorodnitsyn, Evgeniy I. Kaptsov, Roman V. Kozlov +2
The paper considers the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. The inviscid, thermally non-conducting medium is modeled by a polyt…
Symmetries, conservation laws, invariant solutions and difference schemes of the one-dimensional Green-Naghdi equations
V. A. Dorodnitsyn, E. I. Kaptsov, S. V. Meleshko
The paper is devoted to the Lie group properties of the one-dimensional Green-Naghdi equations describing the behavior of fluid flow over uneven bottom topography. The bottom topog…
Conservation Laws of the Two-Dimensional Gas Dynamics Equations
E. I. Kaptsov, S. V. Meleshko
Two-dimensional gas dynamics equations in mass Lagrangian coordinates are studied in this paper. The equations describing these flows are reduced to two Euler-Lagrange equations. U…