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    Interaction of Kortewegâ-de Vries solitons with external sources

    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

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    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
    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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