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16 papers · 1 filter
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…
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…
One-dimensional MHD flows with cylindrical symmetry: Lie symmetries and conservation laws
Vladimir A. Dorodnitsyn, Evgeniy I. Kaptsov, Roman V. Kozlov +1
A recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. This paper analyses the o…
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…
Group analysis approach for finding reciprocal transformations for the two-dimensional stationary gasdynamics
P. Siriwat, S. V. Meleshko
Equivalence transformations play one of the important roles in continuum mechanics. These transformations reduce the original equations to simpler forms. One of the classes of nonl…
Reciprocal Transformations in Relativistic Gasdynamics. Lie Group Connections
Sergey V. Meleshko, Colin Rogers
Reciprocal transformations associated with admitted conservation laws were originally used to derive invariance properties in non-relativistic gasdynamics and applied to obtain red…