Group classification of the two-dimensional magnetogasdynamics equations in Lagrangian coordinates

TL;DR

This paper performs a comprehensive group classification of two-dimensional magnetogasdynamics equations in Lagrangian coordinates, facilitating the construction of invariant solutions and conservation laws for inviscid, nonthermal polytropic gases.

Contribution

It provides the first complete group classification of these equations in Lagrangian coordinates, reducing variables and enabling advanced solution methods.

Findings

Complete group classification achieved

Reduction in dependent variables using Lagrangian coordinates

Foundation for constructing invariant solutions and conservation laws

Abstract

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 Noether's theorem.