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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 4, Pages 725–728 (Mi zvmmf161)  
Influence of cubic nonlinearity on the dispersion relation for long waves on a water surface

A. V. Astashenok, A. A. Zaitsev

Kurchatov Institute of Atomic Energy, Kaliningrad State University, ul. A. Nevskogo 14, Kaliningrad, 236041, Russia
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Abstract: The influence of cubic nonlinearity on the dispersion relation for long waves on a water surface is analyzed. In the long wavelength limit, it is shown that the dispersion relation is not affected by the cubic terms. The results are compared with the dispersion relation for stationary solutions to the Korteweg–de Vries equation.
Key words: shallow water theory of a fluid, cubic nonlinearities in the wave equations, dispersion relation, approximate perturbation technique.
Received: 11.11.2005
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 4, Pages 688–691
DOI: https://doi.org/10.1134/S0965542508040155
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: A. V. Astashenok, A. A. Zaitsev, “Influence of cubic nonlinearity on the dispersion relation for long waves on a water surface”, Zh. Vychisl. Mat. Mat. Fiz., 48:4 (2008), 725–728; Comput. Math. Math. Phys., 48:4 (2008), 688–691
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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