# Soliton transmutations in KdV--Burgers layered media

## TL;DR

This paper investigates how solitons behave when passing through layered media with dissipation, revealing new phenomena such as bi-soliton formation, amplitude changes with negative dissipation, and shock-to-oscillation transformation.

## Contribution

It introduces novel effects of soliton interactions with dissipative barriers in layered media, including bi-soliton creation and amplitude enhancement due to negative dissipation.

## Key findings

- Solitons become bi-solitons after passing through dissipative barriers.
- Negative dissipation leads to increased soliton amplitude and velocity.
- Shock waves transform into quasi-harmonic oscillations in non-dissipative layers.

## Abstract

We study the behavior of the soliton which, while moving in non-dissipative medium encounters a barrier with dissipation. The modelling included the case of a finite dissipative layer as well as a wave passing from a dissipative layer into a non-dissipative one and vice versa. New effects are presented in the case of numerically finite barrier on the soliton path: first, if the form of dissipation distribution has a form of a frozen soliton, the wave that leaves the dissipative barrier becomes a bi-soliton and a reflection wave arises as a comparatively small and quasi-harmonic 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 transforms into a quasi-harmonic oscillation known for the KdV.