Formation of wave packets in the Ostrovsky equation for both normal and anomalous dispersion
Article
Article Title | Formation of wave packets in the Ostrovsky equation for both normal and anomalous dispersion |
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ERA Journal ID | 39856 |
Article Category | Article |
Authors | Grimshaw, Roger (Author), Stepanyants, Yury (Author) and Alias, Azwani (Author) |
Journal Title | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
Journal Citation | 472 (2185), pp. 1-20 |
Number of Pages | 20 |
Year | 2016 |
Publisher | Royal Society Publishing |
Place of Publication | United Kingdom |
ISSN | 1364-5021 |
1471-2946 | |
Digital Object Identifier (DOI) | https://doi.org/10.1098/rspa.2015.0416 |
Web Address (URL) | http://rspa.royalsocietypublishing.org/content/472/2185/20150416 |
Abstract | 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. |
Keywords | soliton; Ostrovsky equation; NLS equation; Korteweg-de Vries equation; envelope soliton; modulation instability; numerical calculation |
ANZSRC Field of Research 2020 | 401207. Fundamental and theoretical fluid dynamics |
370803. Physical oceanography | |
490109. Theoretical and applied mechanics | |
Public Notes | Files associated with this item cannot be displayed due to copyright restrictions. |
Byline Affiliations | Loughborough University, United Kingdom |
School of Agricultural, Computational and Environmental Sciences | |
University of Malaysia, Terengganu, Malaysia | |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q33w7/formation-of-wave-packets-in-the-ostrovsky-equation-for-both-normal-and-anomalous-dispersion
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