Nonlinear waves in layered media: Solutions of the KdV–Burgers equation

Abstract

Abstract We use the KdV–Burgers equation to model a behaviour of a soliton which, while moving in non-dissipative medium encounters a barrier with dissipation. The modelling included the case of a finite width dissipative layer as well as a wave passing from a non-dissipative layer into a dissipative one. The dissipation results in reducing the soliton amplitude/velocity, and a reflection and refraction occur at the boundary(s) of a dissipative layer. In the case of a finite width barrier on the soliton path, after the wave leaves the dissipative barrier it retains a soliton form and a reflection wave arises as small and quasi-harmonic oscillations (a breather). The first order approximation in the expansion by the small dissipation parameter is studied.