39 citations · 204 across the 31 of their papers we have counts for
31 papers
Symmetry Approach to Integration of Ordinary Differential Equations with Retarded Argument
Vladimir Dorodnitsyn, Roman Kozlov, Sergey Meleshko
We review studies on the application of Lie group methods to delay ordinary differential equations (DODEs). For first- and second-order DODEs with a single delay parameter that dep…
Delay ordinary differential equations: from Lagrangian approach to Hamiltonian approach
Vladimir Dorodnitsyn, Roman Kozlov, Sergey Meleshko
The paper suggests a Hamiltonian formulation for delay ordinary differential equations (DODEs). Such equations are related to DODEs with a Lagrangian formulation via a delay analog…
Lagrangian formalism and Noether-type theorems for second-order delay ODEs
Vladimir A. Dorodnitsyn, Roman V. Kozlov, Sergey V. Meleshko
The Lagrangian formalism for variational problem for second-order delay ordinary differential equations (DODEs) is developed. The Noether-type operator identities and theorems for…
Invariant Finite-Difference Schemes for Cylindrical One-Dimensional MHD Flows with Conservation Laws Preservation
E. I. Kaptsov, V. A. Dorodnitsyn, S. V. Meleshko
On the basis of the recent group classification of the one-dimensional magnetohydrodynamics (MHD) equations in cylindrical geometry, the construction of symmetry-preserving finite-…
Group classification of the two-dimensional magnetogasdynamics equations in Lagrangian coordinates
S. V. Meleshko, E. I. Kaptsov, S. Moyo +1
The present paper is devoted to the group classification of magnetogasdynamics equations in which dependent variables in Euler coordinates depend on time and two spatial coordinate…
Symmetries and conservation laws of the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates
S. V. Meleshko, V. A. Dorodnitsyn, E. I. Kaptsov
Symmetries of the one-dimensional shallow water magnetohydrodynamics equations (SMHD) in Gilman's approximation are studied. The SMHD equations are considered in case of a plane an…