Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki
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Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki, 2011, Volume 94, Issue 12, Pages 921–925 (Mi jetpl2402)  
This article is cited in 14 scientific papers (total in 14 papers)

PLASMA, HYDRO- AND GAS DYNAMICS

Hamiltonian form and solitary waves of the spatial Dysthe equations

F. Fedeleab, D. S. Dutykhc

a School of Civil and Environmental Engineering, Georgia Institute of Technology
b School of Electrical and Computer Engineering, Georgia Institute of Technology
c Universite de Savoie
Full-text PDF (577 kB) Citations (14)
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Abstract: The spatial Dysthe equations describe the envelope evolution of the free-surface and potential of gravity waves in deep waters. Their Hamiltonian structure and new invariants are unveiled by means of a gauge transformation to a new canonical form of the evolution equations. An accurate Fourier-type spectral scheme is used to solve for the wave dynamics and validate the new conservation laws, which are satisfied up to machine precision. Moreover, traveling waves are numerically constructed using the Petviashvili method. It is shown that their collision appears inelastic, suggesting the non-integrability of the Dysthe equations.
Received: 17.10.2011
English version:
Journal of Experimental and Theoretical Physics Letters, 2011, Volume 94, Issue 12, Pages 840–844
DOI: https://doi.org/10.1134/S0021364011240039
Bibliographic databases:
Document Type: Article
Language: English
Citation: F. Fedele, D. S. Dutykh, “Hamiltonian form and solitary waves of the spatial Dysthe equations”, Pis'ma v Zh. Èksper. Teoret. Fiz., 94:12 (2011), 921–925; JETP Letters, 94:12 (2011), 840–844
Citation in format AMSBIB
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\paper Hamiltonian form and solitary waves of the spatial Dysthe equations
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\issue 12
\pages 921--925
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\pages 840--844
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Письма в Журнал экспериментальной и теоретической физики Pis'ma v Zhurnal Иksperimental'noi i Teoreticheskoi Fiziki
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