Emergence of envelop solitary waves from initial localised pulses within the Ostrovsky equation

Grimshaw, R. H. J. and Stepanyants, Y. A. ORCID: https://orcid.org/0000-0003-4546-0310 (2020) Emergence of envelop solitary waves from initial localised pulses within the Ostrovsky equation. Radiophysics and Quantum Electronics, 63 (1). pp. 21-28. ISSN 0033-8443


Abstract

We study the emergence of steady wave packets in the form of envelope solitary waves (envelope solitons) which evolve from localized pulse-type initial conditions in the long-term evolution within the framework of the Ostrovsky equation. Ostrovsky equation derived in 1978 describes weakly nonlinear oceanic waves affected by the Earth’s rotation. Subsequently it became clear that this equation is universal, and is widely used for the description of waves in various settings. It is well-known that in applications to media with a negative small-scale dispersion this equation does not possess steady solitary wave solutions. In particular, the evolution of an initial Korteweg-de Vries (KdV) soliton results in the emergence of envelope solitons which can be described by the nonlinear Schr¨odinger equation (NLS) when the amplitude of the initial KdV soliton is sufficiently small. However, the derivation of the corresponding NLS still has not been sufficiently comprehensive, which resulted in contradiction with some numerical simulations. Here, we revisit this problem and suggest a new approach to the construction of the emerging envelope solitons.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Permanent restricted access to published version, in accordance with the copyright policy of the publisher.
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 -)
Faculty/School / Institute/Centre: Current - Institute for Advanced Engineering and Space Sciences (1 Aug 2018 -)
Date Deposited: 01 Nov 2020 23:47
Last Modified: 15 Feb 2021 23:34
Uncontrolled Keywords: envelop solitary waves; Ostrovsky equation; soliton; waves in rotating fluid
Fields of Research (2008): 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
Fields of Research (2020): 40 ENGINEERING > 4012 Fluid mechanics and thermal engineering > 401207 Fundamental and theoretical fluid dynamics
37 EARTH SCIENCES > 3708 Oceanography > 370803 Physical oceanography
49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490109 Theoretical and applied mechanics
Socio-Economic Objectives (2008): 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: https://doi.org/10.1007/s11141-020-10031-1
URI: http://eprints.usq.edu.au/id/eprint/40018

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