Soliton transmutations in KdV--Burgers layered media
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.
Keywords
Cite
@article{arxiv.1907.10489,
title = {Soliton transmutations in KdV--Burgers layered media},
author = {Alexey Samokhin},
journal= {arXiv preprint arXiv:1907.10489},
year = {2019}
}
Comments
8 pages;14 figures; 4 movies attached. To view attachments, please download .avi source files listed under "Other formats". arXiv admin note: text overlap with arXiv:1707.03649