Modelling Solutions to the Kdv-Burgers Equation in the Case of Non-homogeneous Dissipative Media

Abstract

We study the behavior of the soliton which, while moving in non-dissipative medium encounters a barrier with finite dissipation. The modelling included the case of a finite dissipative layer similar to a wave passing through the air-glass-air as well as a wave passing from a non-dissipative layer into a dissipative one (similar to the passage of light from air to water). The dissipation predictably results in reducing the soliton amplitude/velocity, but some new effects occur in the case of finite barrier on the soliton path: after the wave leaves the dissipative barrier it retains a soliton form, yet a reflection wave arises as small and quasi-harmonic oscillations (a breather). The breather spreads faster than the soliton as moves through the barrier.