Evolution of weak shock waves in non-ideal magnetogasdynamics

The aim of this paper is to analyze the main features of weakly non-linear waves propagating in a compressible, inviscid, non-ideal gas with infinite electrical conductivity modelled by van der Waals equation of state permeated by transverse magnetic field. An asymptotic approach is used to derive the evolution equation, which characterizes the wave phenomena in a high frequency domain. The growth equation of an acceleration wave is derived as a special case. Further, we also discuss the propagation of disturbances in the form of sawtooth profile. The effect of magnetic field and van der Waals parameter on the decay of sawtooth profile is presented. A remarkable difference between planar and nonplanar flows in magnetic case and nonmagnetic case has been drawn. Also the variation in velocity profile between planar and nonplanar flows has been discussed.