The effect of dust on the propagation of a hydromagnetic solitary wave along the magnetic field in a cold collision-free plasma

The effect of dust is studied on the parallel propagation of a solitary hydromagnetic wave in a magnetized, cold, collision-free plasma. The fully nonlinear analysis is based on the Adlam–Allen method. The system of nonlinear differential equations was derived using the assump- tion of massive dust, namely, that the dust velocity is constant and parallel to the background magnetic field. Self-consistent solutions obtained from the model for the lighter particles dynamics and for the resulting electric and magnetic fields are presented, together with the validity range of Mach numbers as a function of dust parameters. In particular, supersonic solutions are possible in scenarios tending to two- component plasmas (positively charged ions and negatively charged dust). The stationary solitary pulse in terms of particle densities, magni- tude of transverse magnetic field, transverse electron–ion velocities, and bipolar electric field is presented. The magnitude of these amplitudes is maximum at the center of wave and minimum at the boundary. Furthermore, it is shown that all the solitary wave amplitudes are decreases with dust parameter.