Plane one-dimensional MHD flows: Symmetries and conservation laws

The paper considers the plane one-dimensional flows for magnetohydrodynamics in mass Lagrangian coordinates. inviscid, thermally non-conducting medium is modeled by a polytropic gas. equations are examined symmetries and conservation laws. For case of finite electric conductivity we establish Lie group classification, i.e. describe all cases $ \sigma ( \rho , p)$ which there symmetry extensions. laws derived direct computation. infinite electrical can be brought into variational form classification performed entropy function as an arbitrary element. Using structure, employ Noether theorem obtaining also given physical variables.