authorea
Authorea
10.22541/au.167213147.72183573/v1
Group classification of the two-dimensional magnetogasdynamics equations
in Lagrangian coordinates
0000-0002-3205-5650
Meleshko
Sergey
Suranaree University of Technology School of Mathematics
Kaptsov
Evgenii
Suranaree University of Technology School of Mathematics
Moyo
S.
Stellenbosch University Faculty of Science
Webb
G. M.
The University of Alabama in Huntsville
27
12
2022
This preprint is available at https://doi.org/10.22541/au.167213147.72183573/v1
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 coordinates. It is assumed
that the continuum is inviscid and nonthermal polytropic gas with
infinite electrical conductivity. The equations are considered in mass
Lagrangian coordinates. Use of Lagrangian coordinates allows reducing
number of dependent variables. The analysis presented in this article
gives complete group classification of the studied equations. This
analysis is necessary for constructing invariant solutions and
conservation laws on the base of Noetherâ€™s theorem.
lagrangian coordinates
lie point symmetries
magnetohydrodynamics