Exact solutions to magnetogasdynamic equations in Lagrangian coordinates

The Lie group of point transformations, which leave the equations for a simplified model of one dimensional ideal gas in magnetogasdynamics invariant, are used to obtain some exact solutions for the governing system of hyperbolic partial differential equations (PDEs). Similarity variables which reduces the governing system of PDEs into system of ordinary differential equations (ODEs) are determined through the transformations. The resulting ODEs are solved analytically to obtain some exact solutions that exhibits space-time dependence. Further, we study the propagation of weak discontinuity through a state characterized by one of the solutions.