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

Ermakov, Andrei and Stepanyants, Yury ORCID: https://orcid.org/0000-0003-4546-0310 (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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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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Published version deposited in accordance with the copyright policy of the publisher.
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences (1 Jul 2013 - 5 Sep 2019)
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences (1 Jul 2013 - 5 Sep 2019)
Date Deposited: 25 Sep 2019 03:28
Last Modified: 15 Feb 2021 23:34
Uncontrolled Keywords: Surface waves; Soliton solutions; Korteweg-de Vries equation; Dynamical systems; Internal waves; Perturbation theory; Asymptotic analysis; Numerical methods
Fields of Research (2008): 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics
09 Engineering > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics
04 Earth Sciences > 0404 Geophysics > 040403 Geophysical Fluid Dynamics
01 Mathematical Sciences > 0102 Applied Mathematics > 010299 Applied Mathematics not elsewhere classified
Fields of Research (2020): 40 ENGINEERING > 4012 Fluid mechanics and thermal engineering > 401207 Fundamental and theoretical fluid dynamics
40 ENGINEERING > 4012 Fluid mechanics and thermal engineering > 401204 Computational methods in fluid flow, heat and mass transfer (incl. computational fluid dynamics)
40 ENGINEERING > 4012 Fluid mechanics and thermal engineering > 401208 Geophysical and environmental fluid flows
49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490199 Applied mathematics not elsewhere classified
Identification Number or DOI: https://doi.org/10.1063/1.5063561
URI: http://eprints.usq.edu.au/id/eprint/37113

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