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Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki, 2013, Volume 98, Issue 11, Pages 826–829
DOI: https://doi.org/10.7868/S0370274X13230173
(Mi jetpl3599)
 

This article is cited in 11 scientific papers (total in 11 papers)

METHODS OF THEORETICAL PHYSICS

Extreme waves statistics for Ablowitz-Ladik system

D. S. Agafontsevab

a P. P. Shirshov Institute of Oceanology, Russian Academy of Sciences
b Novosibirsk State University
References:
Abstract: We examine statistics of waves for the problem of modulation instability development in the framework of discrete integrable Ablowitz–Ladik (AL) system. Modulation instability depends on one free parameter $h$ that has the meaning of the coupling between the nodes on the lattice. For strong coupling $h\ll 1$ the probability density functions (PDFs) for waves amplitudes coincide with that for the continuous classical Nonlinear Schrodinger (NLS) equation; the PDFs for both systems are very close to Rayleigh ones. When the coupling is weak $h\sim 1$, there appear highly localized waves with very large amplitudes, that drastically change the PDFs to significantly non-Rayleigh ones, with so-called “fat tails” when the probability of a large wave occurrence is by several orders of magnitude higher than that predicted by the linear theory. Evolution of amplitudes for such rogue waves with time is similar to that of the Peregrine solution for the classical NLS equation.
Received: 17.10.2013
English version:
Journal of Experimental and Theoretical Physics Letters, 2013, Volume 98, Issue 11, Pages 731–734
DOI: https://doi.org/10.1134/S0021364013240028
Bibliographic databases:
Document Type: Article
Language: English
Citation: D. S. Agafontsev, “Extreme waves statistics for Ablowitz-Ladik system”, Pis'ma v Zh. Èksper. Teoret. Fiz., 98:11 (2013), 826–829; JETP Letters, 98:11 (2013), 731–734
Citation in format AMSBIB
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  • This publication is cited in the following 11 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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