Simple waves of the two dimensional compressible Euler equations in magnetohydrodynamics

In this paper, we are concerned with the simple waves for the two dimensional (2D) compressible Euler equations in magnetohydrodynamics. By using the sufficient conditions for the existence of characteristic decompositions to the general quasilinear strictly hyperbolic systems, we establish that any wave adjacent to a constant state must be a simple wave to the two dimensional compressible magnetohydrodynamics system for a polytropic Van der Waals gas and a polytropic perfect gas.