Interaction of Finite Perturbations with the Front and Singularity of the Profile of a Nonlinear Wave in a Dissipative Medium

Abstract The interaction of a short pulse with three types wave profiles in nonlinear dissipative medium are described: stationary shock front finite width, nonstationary forming front, and “stationary” the profile which contains singularity. Exact solutions to Burgers equation used, describe these interactions, as well symmetry properties this equation.