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

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