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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 2, Page 281
DOI: https://doi.org/10.7868/S0044466913020075 (Mi zvmmf9784) 		 
This article is cited in 27 scientific papers (total in 27 papers)

Geometric numerical schemes for the KdV equation

D. Dutykha, M. Chhaya, F. Fedeleb

a Universite de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France
b School of Civil and Environmental Engineering and School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, USA
Full-text PDF (95 kB) Citations (27)
DOI: https://doi.org/10.7868/S0044466913020075
Abstract: Geometric discretizations that preserve certain Hamiltonian structures at the discrete level has been proven to enhance the accuracy of numerical schemes. In particular, numerous symplectic and multi-symplectic schemes have been proposed to solve numerically the celebrated Korteweg-de Vries equation. In this work, we show that geometrical schemes are as much robust and accurate as Fourier-type pseudospectral methods for computing the long-time KdV dynamics, and thus more suitable to model complex nonlinear wave phenomena.
Key words: geometric numerical schemes, Hamiltonian structures, pseudo-spectral methods, Korteweg-de Vries equation, symplectic and multi-symplectic schemes, wave turbulence.
Received: 17.05.2012
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 2, Pages 221–236
DOI: https://doi.org/10.1134/S0965542513020103
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: English
Citation: D. Dutykh, M. Chhay, F. Fedele, “Geometric numerical schemes for the KdV equation”, Zh. Vychisl. Mat. Mat. Fiz., 53:2 (2013), 281; Comput. Math. Math. Phys., 53:2 (2013), 221–236
Citation in format AMSBIB
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    • This publication is cited in the following 27 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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