Beyond the KdV: post-explosion development

Ostrovsky, L. and Pelinovsky, E. and Shrira, V. and Stepanyants, Y. (2015) Beyond the KdV: post-explosion development. Chaos, 25 (9). pp. 1-13. ISSN 1054-1500

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Abstract

Several threads of the last 25 years’ developments in nonlinear wave theory that stem from the classical Korteweg–de Vries (KdV) equation are surveyed. The focus is on various generalizations of the KdV equation which include higher-order nonlinearity, large-scale dispersion, and a nonlocal integral dispersion. We also discuss how relatively simple models can capture strongly nonlinear dynamics and how various modifications of the KdV equation lead to qualitatively new, non-trivial solutions and regimes of evolution observable in the laboratory and in nature. As the main physical example, we choose internal gravity waves in the ocean for which all these models are applicable and have genuine importance. We also briefly outline the authors’ view of the future development of the chosen lines of nonlinear wave theory.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Published version deposited in accordance with the copyright policy of the publisher.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 19 Apr 2016 23:49
Last Modified: 28 Sep 2016 01:55
Uncontrolled Keywords: nonlinear model; water wave; solitary wave; modulation; breather; KdV equation; dispersion
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: D Environment > 96 Environment > 9610 Natural Hazards > 961006 Natural Hazards in Marine Environments
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: 10.1063/1.4927448
URI: http://eprints.usq.edu.au/id/eprint/27586

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