Search Results - "Meleshko, S. V."

Conservation laws of the two-dimensional relativistic gas dynamics equations by Nakpim, W., Meleshko, S.V.

“…Two-dimensional relativistic gas dynamics equations are considered in the paper. Using a suitable Lagrangian found by solving the Helmholtz problem, the…”
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GROUP CLASSIFICATION OF THE TWO-DIMENSIONAL GREEN–NAGHDI EQUATIONS WITH A TIME-DEPENDENT BOTTOM TOPOGRAPHY by Meleshko, S. V., Siriwat, P.

“…The two-dimensional Green–Naghdi equations are studied for the case of uneven bottom topography. The bottom topography function can depend on time. Group…”
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One class of MHD equations: Conservation laws and exact solutions by Kaptsov, E. I., Meleshko, S. V.

“…Abstract The paper analyzes one of the models of equations of magnetohydrodynamics (MHD) derived earlier. The model was obtained as a result of group…”
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Conservation laws of the two-dimensional gas dynamics equations by Kaptsov, E.I., Meleshko, S.V.

“…Two-dimensional gas dynamics equations in mass Lagrangian coordinates are studied in this paper. The equations describing these flows are reduced to two…”
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On the complete group classification of the one-dimensional nonlinear Klein-Gordon equation with a delay by Long, Feng-Shan, Meleshko, S. V.

“…This research gives a complete Lie group classification of the one‐dimensional nonlinear delay Klein–Gordon equation. First, the determining equations are…”
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Symmetries, Conservation Laws, Invariant Solutions and Difference Schemes of the One-dimensional Green-Naghdi Equations by Dorodnitsyn, V. A., Kaptsov, E. I., Meleshko, S. V.

“…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…”
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APPLICATION OF THE METHOD OF DIFFERENTIAL CONSTRAINTS TO SYSTEMS OF EQUATIONS WRITTEN IN RIEMANN INVARIANTS by Meleshko, S. V., Shultz, E.

“…Solutions of one-dimensional equations of gas dynamics and the equations describing the behavior of a nonlinear elastic material are reduced to solving a…”
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Symmetry analysis of the nonlinear two‐dimensional Klein–Gordon equation with a time‐varying delay by Long, Feng‐Shan, Meleshko, S. V.

“…The group analysis method is applied to the two‐dimensional nonlinear Klein–Gordon equation with time‐varying delay. Determining equations for equations with a…”
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Group classification of the two-dimensional shallow water equations with the beta-plane approximation of coriolis parameter in Lagrangian coordinates by Meleshko, S.V., Samatova, N.F.

“…•Analysis of the shallow water equations in Lagrangian coordinates.•Complete group classification of the equations with uneven bottom.•New conservation laws in…”
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Reciprocal transformations of the one-dimensional magnetogasdynamics by Meleshko, S.V.

“…Equivalence transformations play one of the important roles in continuum mechanics. These transformations reduce the original equations to simpler forms. One…”
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Analysis of the one-dimensional Euler–Lagrange equation of continuum mechanics with a Lagrangian of a special form by Kaptsov, EI, Meleshko, SV

“…The equations describing the flow of a one-dimensional continuum in Lagrangian coordinates are studied in this paper by the group analysis method. They are…”
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On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium by Meleshko, S.V., Moshkin, N.P., Pukhnachev, V.V.

“…Unsteady two-dimensional flows of incompressible viscoelastic Maxwell medium with upper, low and corotational convective derivatives in the rheological…”
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Group Analysis of the One-Dimensional Gas Dynamics Equations in Lagrangian Coordinates and Conservation Laws by Kaewmanee, C., Meleshko, S. V.

“…A group analysis of the second-order equation including the one-dimensional gas dynamics equations in Lagrangian coordinates as a particular case is performed…”
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On group classification of normal systems of linear second-order ordinary differential equations by Meleshko, S.V., Moyo, S.

“…•Group classification of systems of linear second-order ordinary differential equations with inconstant coefficients is studied.•The group classification is…”
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Conservation laws of the one-dimensional equations of relativistic gas dynamics in Lagrangian coordinates by Nakpim, W., Meleshko, S.V.

“…The present paper is focused on the analysis of the one-dimensional relativistic gas dynamics equations. The studied equations are considered in Lagrangian…”
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Solutions of generalized simple wave type of magnetic fluid by Meleshko, S.V., Moyo, S., Webb, G.M.

“…•Using the method of differential constraints generalized simple waves are studied.•Finding generalized simple waves solutions reduces to integrating a system…”
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Complete group classification of systems of two linear second-order ordinary differential equations: the algebraic approach by Mkhize, T. G., Moyo, S., Meleshko, S. V.

“…We give a complete group classification of the general case of linear systems of two second‐order ordinary differential equations. The algebraic approach is…”
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On the complete group classification of the reaction–diffusion equation with a delay by Meleshko, S.V., Moyo, S.

“…The reaction–diffusion delay differential equation u t ( x , t ) − u x x ( x , t ) = g ( x , u ( x , t ) , u ( x , t − τ ) ) arises in many applications in the…”
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UNSTEADY ONE-DIMENSIONAL FLOWS OF A VIBRATIONALLY EXCITED GAS by Grigoryev, Yu. N., Meleshko, S. V., Siriwat, P.

“…Complete group analysis of the system of one-dimensional unsteady equations of the dynamics of a vibrationally excited gas is performed in the case of…”
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Application of group analysis to classification of systems of three second-order ordinary differential equations by Suksern, S., Moyo, S., Meleshko, S. V.

“…Here, we give a complete group classification of the general case of linear systems of three second‐order ordinary differential equations excluding the case of…”
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