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    Soliton interaction with external forcing within the Korteweg–de Vries equation


    Ermakov, Andrei and Stepanyants, Yury (2019) Soliton interaction with external forcing within the Korteweg–de Vries equation. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29 (1). 013117. ISSN 1054-1500

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    Official URL: https://doi.org/10.1063/1.5063561


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    Abstract

    We revise the solutions of the forced Korteweg–de Vries equation describing a resonant interaction of a solitary wave with external pulse-type perturbations. In contrast to previous work where only the limiting cases of a very narrow forcing in comparison with the initial soliton or a very narrow soliton in comparison with the width of external perturbation were studied, we consider here an arbitrary relationship between the widths of soliton and external perturbation of a relatively small amplitude. In many particular cases, exact solutions of the forced Korteweg–de Vries equation can be obtained for the specific forcings of arbitrary amplitude. We use the earlier developed asymptotic method to derive an approximate set of equations up to the second-order on a small parameter characterising the amplitude of external force. The analysis of exact solutions of the derived equations is presented and illustrated graphically. It is shown that the theoretical outcomes obtained by the asymptotic method are in a good agreement with the results of direct numerical modeling within the framework of forced Korteweg–de Vries equation

    Item Type: Article
    Additional Information: Cite as: Andrei Ermakov and Yury Stepanyants , "Soliton interaction with external forcing within the Korteweg–de Vries equation", Chaos 29, 013117 (2019) https://doi.org/10.1063/1.5063561
    Keywords: resonant interaction; solitary wave; arbitrary amplitude;
    Academic Unit: Faculty of Science and Engineering > Electronic Engineering
    Item ID: 16023
    Identification Number: https://doi.org/10.1063/1.5063561
    Depositing User: Dr Andrei Ermakov
    Date Deposited: 31 May 2022 11:34
    Journal or Publication Title: Chaos: An Interdisciplinary Journal of Nonlinear Science
    Publisher: AIP Publishing
    Refereed: Yes
    URI:

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