Soliton transmutations in KdV–Burgers layered media

Abstract

We study the behaviour of the soliton which, while travelling in non-dissipative medium encounters a barrier with dissipation. New effects are presented in the case of numerically finite barrier on the soliton path: first, if the dissipation distribution has a form of a frozen soliton, the wave leaving the dissipative barrier emerges as a bi-soliton and a reflection wave is a comparatively small oscillation. Second, if the dissipation is negative (the wave, instead of loosing energy, is pumped with it) the passed wave is a soliton of a greater amplitude and velocity. Third, when the travelling wave solution of the KdV–Burgers (it is a shock wave in a dissipative region) enters a non-dissipative layer this shock wave transforms into a quasi-harmonic oscillation.