Interaction of solitons with long waves in a rotating fluid

Ostrovsky, L. A. and Stepanyants, Y. A. (2016) Interaction of solitons with long waves in a rotating fluid. Physica D: Nonlinear Phenomena , 333. pp. 266-275. ISSN 0167-2789

Abstract

Interaction of a soliton with long background waves is studied within the framework of rotation modified Korteweg -de Vries (rKdV) equation. Using the asymptotic method for solitons propagating in the field of a long background wave we derive a set of ODEs describing soliton amplitude and phase with respect to the background wave. The shape of the background wave may range from a sinusoid to the limiting profile representing a periodic sequence of parabolic arcs. We analyse energy exchange between a soliton and the long wave taking radiation losses into account. It is shown that the losses can be compensated by energy pumping from the long wave and, as the result, a stationary soliton can exist, unlike the case when there is no variable background. A more complex case when a free long wave attenuates due to the energy consumption by a soliton is also considered. Some of the analytical results are compared with the results of direct numerical calculations within the framework of the rKdV equation.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Files associated with this item cannot be displayed due to copyright restrictions.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 12 Sep 2016 06:22
Last Modified: 20 Oct 2016 03:58
Uncontrolled Keywords: Rotating fluid, Soliton, Radiative losses, Terminal decay, Energy balance, Numerical calculations
Fields of Research : 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics
04 Earth Sciences > 0405 Oceanography > 040503 Physical Oceanography
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
E Expanding Knowledge > 97 Expanding Knowledge > 970104 Expanding Knowledge in the Earth Sciences
Identification Number or DOI: 10.1016/j.physd.2016.02.008
URI: http://eprints.usq.edu.au/id/eprint/29534

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