Ermakov, Andrei and Stepanyants, Y. A.
(2018)
Interaction of Kortewegâ-de Vries solitons with external sources.
Proceedings of the 21st Australasian Fluid Mechanics Conference.
ISSN 978-0-646-59784-3
Abstract
We consider the problem of interaction of a solitary wave with
a moving external source within the framework of Korteweg–
de Vries (KdV) equation. We show that for certain profiles
of external source the problem has exact solutions in the form
of a stationary solitary waves coupled with the force. For the
solitary waves which are not trapped by the external force of
a small amplitude we obtain approximate solutions by means
of the asymptotic method and analyse solutions with the arbi-
trary relationship between the widths of forcing function and
solitary wave. Results obtained agree well with the results of
previous works where only the limiting cases of very narrow
or infinitely wide forcing as compared with the width of soli-
tary wave were studied. Several new regimes of soliton interac-
tion with width the forcing have been revealed. The theoretical
results have been validated by the direct numerical modelling
within the framework of forced KdV equation.
| Item Type: |
Article
|
| Keywords: |
Interaction; Kortewegâ-de Vries solitons; external sources; |
| Academic Unit: |
Faculty of Science and Engineering > Electronic Engineering |
| Item ID: |
16624 |
| Depositing User: |
Dr Andrei Ermakov
|
| Date Deposited: |
18 Oct 2022 14:11 |
| Journal or Publication Title: |
Proceedings of the 21st Australasian Fluid Mechanics Conference |
| Publisher: |
Australasian Fluid Mechanics Society |
| Refereed: |
Yes |
| URI: |
|
| Use Licence: |
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available
here |
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