Evolution of planar and cylindrically symmetric magneto-acoustic waves in a van der Waals fluid

We consider a quasilinear system of partial differential equations (PDEs) governing the one-dimensional unsteady planar and cylindrically symmetric motion of an electrically conducting van der Waals fluid permeated with a transverse magnetic field. An asymptotic method is used to derive an evolution equation that governs the wave amplitude in the far field. Our main objective is to study the evolution equation, and to investigate as to how the presence of magnetic field and geometrical spreading (in cylindrical case) along with the cubic nonlinearity, inherently present in the system, influence the wave structure that finally develops.