On stationary solutions of the reduced Gardner–Ostrovsky equation

Obregon, Maria and Stepanyants, Yury (2014) On stationary solutions of the reduced Gardner–Ostrovsky equation. Discontinuity, Nonlinearity and Complexity, 3 (4). pp. 445-456. ISSN 2164-6376

Abstract

The detailed analysis of stationary solutions of the reduced Gardner–Ostrovsky (GO) equation is presented. The GO equation is the popular model for the description of large-amplitude internal oceanic waves affected by Earth’s rotation. Its reduced version in which the small-scale dispersion is neglected is used when very long internal waves are considered. The equation is also applicable to other types of nonlinear waves in various media (plasma, optical media, relaxing media, etc.) when the large-scale dispersion plays a dominant role in comparison with the small-scale dispersion. Balancing the nonlinear effect such dispersion gives rise to existence of stationary waves, both periodic and non-periodic. It is shown that only smooth periodic waves make physical sense. Systematic analysis of stationary solutions to the GO equation and their categorisation is presented.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 07 Dec 2014 03:01
Last Modified: 08 Apr 2015 06:34
Uncontrolled Keywords: Gardner–Ostrovsky equation; periodic waves; stationary solution; rotational dispersion; oceanic waves
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: 10.5890/DNC.2014.12.007
URI: http://eprints.usq.edu.au/id/eprint/26419

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