On the evolution of magnetic shock wave in the mixture of gas and small solid dust particles

The paper aims to analyze the evolutionary behavior of weakly nonlinear waves propagating in one-dimensional unsteady flow of perfectly conducting compressible fluid subjected to a transverse magnetic field with dust particles. The method of progressive wave approach is utilized to determine the evolution equation characterizing the propagation of wave and also obtained the condition for first wave breaking at finite time. Further, we analyze the behavior of acceleration wave propagating in the medium considered. Also, the propagation of disturbances in the form of sawtooth wave (half N-wave) is studied here. It is observed that the presence of mass fraction of solid particles (k(p)) and beta both causes to slow down the decay process. Also, the effect of axial magnetic field is to increase the growth rate of sawtooth wave (Half N-wave) as compared to in the absence of axial magnetic field. Further, the effect of magnetic field is to slow down the decay process in the presence of mass fraction of solid particles (k(p)).