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

Khusnutdinova, K. R. and Stepanyants, Y. A. 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). pp. 1-20. ISSN 1070-6631

Abstract

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 is 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.).


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Published version embargoed until 09 Feb 2019 (12 months), in accordance with the copyright policy of the Publisher. 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. and Stepanyants, Y. A. 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). pp. 1-20. and may be found at http://aip.scitation.org/doi/10.1063/1.5009965.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 19 Feb 2018 01:34
Last Modified: 15 May 2018 00:09
Uncontrolled Keywords: water waves, Korteweg–de Vries equation, soliton, numerical modelling
Fields of Research : 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics
01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970102 Expanding Knowledge in the Physical Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.1063/1.5009965
URI: http://eprints.usq.edu.au/id/eprint/33723

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