Propagation of nonlinear magnetoacoustic waves in a compressible medium of finite electrical conductivity

Abstract

We study the one-dimensional propagation of weakly nonlinear waves in a compressible medium of finite electrical conductivity subjected to the action of a magnetic field. We obtain evolution equations that describe the wave processes under small and finite magnetic Reynolds numbers. It is shown that in a medium of finite conductivity the evolution of perturbations in a fluid is described by the modified Burger's equation. We find the stationary and automodel solution of this equation and use them as the basis for analyzing the influence of effects of electrical conductivity on the structure of weak shock waves.