[en] The authors 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. Evolution equations are obtained 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. The stationary and automodel solution of this equation are found and used as the basis for analyzing the influence of effects of electrical conductivity on the structure of weak shock waves. 9 refs