Dispersion of long gravity-capillary surface waves and asymptotic equations for solitons

Stepanyants, Yury (2005) Dispersion of long gravity-capillary surface waves and asymptotic equations for solitons. Proceedings of the Russian Academy of Engineering Sciences Series: Applied Mathematics and Mechanics, 14. pp. 33-40.

Abstract

It is shown that in the description of long surface gravity-capillary waves, accounting for air density is essential when the fluid depth is close to the critical value. At critical depth the dispersive term of the third order (KdV-dispersion) in the Taylor's series of frequency on wavenumber vanishes due to expostulate actions of gravity and capillary effects. Estimates show that in the critical case the dispersive term of the second order (BO-dispersion), rather than the fifth order, as was thought before, becomes determinative. The main dispersive term, in the corresponding evolution equation for weakly nonlinear perturbations, determines a structure of solitary waves. Solitary wave solutions numerically obtained for the combined BO-KdV equation, as well as their Fourier spectra, are compared with the known soliton solutions of the BO and KdV equations.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: (Published in Russian) ISBN: 5-93496-048-2.
Depositing User: Assoc Prof Yury Stepanyants
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 02 Sep 2011 03:42
Last Modified: 03 Jul 2013 00:45
Uncontrolled Keywords: surface wave, capillary effect, air density, shallow water, critical depth, dispersion relation, evolution equation, solitary wave, numerical modelling
Fields of Research (FOR2008): 04 Earth Sciences > 0405 Oceanography > 040503 Physical Oceanography
01 Mathematical Sciences > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications
01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
Socio-Economic Objective (SEO2008): 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
URI: http://eprints.usq.edu.au/id/eprint/19551

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