Freak waves as a result of modulation instability

Vladimir Zakharov; Andrey Gelash

doi:10.1016/j.piutam.2013.09.014

Freak waves as a result of modulation instability

Vladimir Zakharov, Andrey Gelash

Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

We describe a general N-solitonic solution of the focusing NLSE in the presence of a condensate by using the dressing method. We find a broad class of superregular solitonic solutions which are small perturbations at certain a moment of time. They describe the nonlinear stage of the modulation instability of the condensate and play an important role in the theory of freak waves.

Original language	English (US)
Pages (from-to)	165-175
Number of pages	11
Journal	Procedia IUTAM
Volume	9
DOIs	https://doi.org/10.1016/j.piutam.2013.09.014
State	Published - 2013

Keywords

dressing method
freak waves
modulational instability
nonlinear Schrödinger equation
soliton

ASJC Scopus subject areas

Mechanical Engineering

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10.1016/j.piutam.2013.09.014

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title = "Freak waves as a result of modulation instability",

abstract = "We describe a general N-solitonic solution of the focusing NLSE in the presence of a condensate by using the dressing method. We find a broad class of superregular solitonic solutions which are small perturbations at certain a moment of time. They describe the nonlinear stage of the modulation instability of the condensate and play an important role in the theory of freak waves.",

keywords = "dressing method, freak waves, modulational instability, nonlinear Schr{\"o}dinger equation, soliton",

author = "Vladimir Zakharov and Andrey Gelash",

note = "Funding Information: The authors express deep gratitude to Dr. E.A. Kuznetsov for helpful discussions. This work was supported by: Russian Federation Government Grant (No. 11.G34.31.0035 with Ministry of Education and Science of RF, November 25, 2010), the RFBR (grant no. 12-01-00943), and by the Grant ”Leading Scientific Schools of Russia” (No. 6170.2012.2).",

year = "2013",

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language = "English (US)",

volume = "9",

pages = "165--175",

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issn = "2210-9838",

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TY - JOUR

T1 - Freak waves as a result of modulation instability

AU - Zakharov, Vladimir

AU - Gelash, Andrey

N1 - Funding Information: The authors express deep gratitude to Dr. E.A. Kuznetsov for helpful discussions. This work was supported by: Russian Federation Government Grant (No. 11.G34.31.0035 with Ministry of Education and Science of RF, November 25, 2010), the RFBR (grant no. 12-01-00943), and by the Grant ”Leading Scientific Schools of Russia” (No. 6170.2012.2).

PY - 2013

Y1 - 2013

N2 - We describe a general N-solitonic solution of the focusing NLSE in the presence of a condensate by using the dressing method. We find a broad class of superregular solitonic solutions which are small perturbations at certain a moment of time. They describe the nonlinear stage of the modulation instability of the condensate and play an important role in the theory of freak waves.

AB - We describe a general N-solitonic solution of the focusing NLSE in the presence of a condensate by using the dressing method. We find a broad class of superregular solitonic solutions which are small perturbations at certain a moment of time. They describe the nonlinear stage of the modulation instability of the condensate and play an important role in the theory of freak waves.

KW - dressing method

KW - freak waves

KW - modulational instability

KW - nonlinear Schrödinger equation

KW - soliton

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U2 - 10.1016/j.piutam.2013.09.014

DO - 10.1016/j.piutam.2013.09.014

M3 - Article

AN - SCOPUS:84887426582

SN - 2210-9838

VL - 9

SP - 165

EP - 175

JO - Procedia IUTAM

JF - Procedia IUTAM

ER -

Freak waves as a result of modulation instability

Abstract

Keywords

ASJC Scopus subject areas

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