Formation of wave packets in the Ostrovsky equation for both normal and anomalous dispersion

Grimshaw, Roger and Stepanyants, Yury and Alias, Azwani (2016) Formation of wave packets in the Ostrovsky equation for both normal and anomalous dispersion. Proceeding of the Royal Society A, 472 (2185). pp. 1-20. ISSN 1364-5021


It is well-known that the Ostrovsky equation with normal dispersion does not support steady solitary waves. An initial Korteweg-de Vries solitary wave decays adiabatically through the radiation of long waves and is eventually replaced by an envelope solitary wave whose carrier wave and envelope move with different velocities (phase and group velocities correspondingly). Here we examine the same issue for the Ostrovsky equation with anomalous dispersion when the wave frequency increases with wavenumber in the limit of very short waves. The essential difference is that now there exists a steady solitary wave solution (Ostrovsky soliton), which in the small-amplitude limit can be described asymptotically through the solitary wave solution of a nonlinear Schrodinger equation, based at that wavenumber where the phase and group velocities coincide. Longtime numerical simulations show that the emergence of this steady envelope solitary wave is a very robust feature. The initial Korteweg-de Vries solitary wave transforms rapidly to this envelope solitary wave in a seemingly non-adiabatic manner. The amplitude of the Ostrovsky soliton strongly correlates with the initial Korteweg-de Vries solitary wave.

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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: 04 Jul 2016 01:21
Last Modified: 06 Mar 2018 05:54
Uncontrolled Keywords: soliton; Ostrovsky equation; NLS equation; Korteweg-de Vries equation; envelope soliton; modulation instability; numerical calculation
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
Identification Number or DOI: 10.1098/rspa.2015.0416

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