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

TL;DR

This paper models the behavior of solitons in non-homogeneous dissipative media, revealing how dissipation affects soliton amplitude, velocity, and generates reflection waves with breather oscillations.

Contribution

It introduces a novel model for soliton dynamics in media with finite dissipative layers, analyzing effects like reflection and breather formation.

Findings

Dissipation reduces soliton amplitude and velocity.

Reflection waves and breathers form after passing through dissipative barriers.

Breathers spread faster than solitons in 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.