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Soliton solutions to the fifth-order Korteweg–de Vries equation and their applications to surface and internal water waves

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posted on 2018-02-09, 08:56 authored by Karima KhusnutdinovaKarima Khusnutdinova, Yury Stepanyants, Matt Tranter
We study solitary wave solutions of the fifth-order Korteweg–de Vries equation which contains, besides the traditional quadratic nonlinearity and third-order dispersion, additional terms including cubic nonlinearity and fifth-order linear dispersion, as well as two nonlinear dispersive terms. An exact solitary wave solution to this equation is derived and the dependence of its amplitude, width and speed on the parameters of the governing equation are studied. It is shown that the derived solution can represent either an embedded or regular soliton depending on the equation parameters. The nonlinear dispersive terms can drastically influence the existence of solitary waves, their nature (regular or embedded), profile, polarity, and stability with respect to small perturbations. We show, in particular, that in some cases embedded solitons can be stable even with respect to interactions with regular solitons. The results obtained are applicable to surface and internal waves in fluids, as well as to waves in other media (plasma, solid waveguides, elastic media with microstructure, etc.).

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Physics of Fluids

Citation

KHUSNUTDINOVA, K.R., STEPANYANTS, Y. and TRANTER, M.R., 2018. Soliton solutions to the fifth-order Korteweg–de Vries equation and their applications to surface and internal water waves. Physics of Fluids, 30 (2), 022104.

Publisher

AIP Publishing

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

2018-01-21

Publication date

2018

Notes

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in KHUSNUTDINOVA, K.R., STEPANYANTS, Y. and TRANTER, M.R., 2018. Soliton solutions to the fifth-order Korteweg–de Vries equation and their applications to surface and internal water waves. Physics of Fluids, 30 (2), 022104 and may be found at https://doi.org/10.1063/1.5009965.

ISSN

1070-6631

eISSN

1089-7666

Language

  • en

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