Quasibreathers in the MMT model

A. Pushkarev; V. E. Zakharov

doi:10.1016/j.physd.2013.01.003

Quasibreathers in the MMT model

A. Pushkarev, V. E. Zakharov

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

14 Scopus citations

Abstract

We report numerical detection of a new type of localized structures in the frame of Majda-McLaughlin-Tabak (MMT) model adjusted for description of essentially nonlinear gravity waves on the surface of ideal deep water. These structures-quasibreathers or oscillating quasisolitons-can be treated as groups of freak waves closely resembling experimentally observed "Three Sisters" wave packets on the ocean surface. The MMT model has quasisolitonic solutions. Unlike NLSE solitons, MMT quasisolitons are permanently backward radiating energy, but nevertheless do exist during thousands of carrier wave periods. Quasisolitons of small amplitude are regular and stable, but large-amplitude ones demonstrate oscillations of amplitude and spectral shape. This effect can be explained by periodic formation of weak collapses, carrying out negligibly small amount of energy. We call oscillating quasisolitons "quasibreathers".

Original language	English (US)
Pages (from-to)	55-61
Number of pages	7
Journal	Physica D: Nonlinear Phenomena
Volume	248
Issue number	1
DOIs	https://doi.org/10.1016/j.physd.2013.01.003
State	Published - Apr 1 2013
Externally published	Yes

Keywords

Breathers
Freak waves
Nonlinear Schrödinger equation
Singularities
Solitons

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/j.physd.2013.01.003

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title = "Quasibreathers in the MMT model",

abstract = "We report numerical detection of a new type of localized structures in the frame of Majda-McLaughlin-Tabak (MMT) model adjusted for description of essentially nonlinear gravity waves on the surface of ideal deep water. These structures-quasibreathers or oscillating quasisolitons-can be treated as groups of freak waves closely resembling experimentally observed {"}Three Sisters{"} wave packets on the ocean surface. The MMT model has quasisolitonic solutions. Unlike NLSE solitons, MMT quasisolitons are permanently backward radiating energy, but nevertheless do exist during thousands of carrier wave periods. Quasisolitons of small amplitude are regular and stable, but large-amplitude ones demonstrate oscillations of amplitude and spectral shape. This effect can be explained by periodic formation of weak collapses, carrying out negligibly small amount of energy. We call oscillating quasisolitons {"}quasibreathers{"}.",

keywords = "Breathers, Freak waves, Nonlinear Schr{\"o}dinger equation, Singularities, Solitons",

author = "A. Pushkarev and Zakharov, {V. E.}",

note = "Funding Information: This work was sponsored by ONR grant N00014-10-1-0991 , NSF grant # 1130450 , Russian Government contract 11.9.34.31.0035, RFBR grant 12-01-00943 , the Program of the RAS Presidium “Fundamental Problems of Nonlinear Dynamics in Mathematical and Physical Sciences” and the “Leading scientific schools of Russia” grant NSh 6170.2012.2 . Authors gratefully acknowledge continuous support of these foundations. ",

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doi = "10.1016/j.physd.2013.01.003",

language = "English (US)",

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AU - Pushkarev, A.

AU - Zakharov, V. E.

N1 - Funding Information: This work was sponsored by ONR grant N00014-10-1-0991 , NSF grant # 1130450 , Russian Government contract 11.9.34.31.0035, RFBR grant 12-01-00943 , the Program of the RAS Presidium “Fundamental Problems of Nonlinear Dynamics in Mathematical and Physical Sciences” and the “Leading scientific schools of Russia” grant NSh 6170.2012.2 . Authors gratefully acknowledge continuous support of these foundations.

PY - 2013/4/1

Y1 - 2013/4/1

N2 - We report numerical detection of a new type of localized structures in the frame of Majda-McLaughlin-Tabak (MMT) model adjusted for description of essentially nonlinear gravity waves on the surface of ideal deep water. These structures-quasibreathers or oscillating quasisolitons-can be treated as groups of freak waves closely resembling experimentally observed "Three Sisters" wave packets on the ocean surface. The MMT model has quasisolitonic solutions. Unlike NLSE solitons, MMT quasisolitons are permanently backward radiating energy, but nevertheless do exist during thousands of carrier wave periods. Quasisolitons of small amplitude are regular and stable, but large-amplitude ones demonstrate oscillations of amplitude and spectral shape. This effect can be explained by periodic formation of weak collapses, carrying out negligibly small amount of energy. We call oscillating quasisolitons "quasibreathers".

AB - We report numerical detection of a new type of localized structures in the frame of Majda-McLaughlin-Tabak (MMT) model adjusted for description of essentially nonlinear gravity waves on the surface of ideal deep water. These structures-quasibreathers or oscillating quasisolitons-can be treated as groups of freak waves closely resembling experimentally observed "Three Sisters" wave packets on the ocean surface. The MMT model has quasisolitonic solutions. Unlike NLSE solitons, MMT quasisolitons are permanently backward radiating energy, but nevertheless do exist during thousands of carrier wave periods. Quasisolitons of small amplitude are regular and stable, but large-amplitude ones demonstrate oscillations of amplitude and spectral shape. This effect can be explained by periodic formation of weak collapses, carrying out negligibly small amount of energy. We call oscillating quasisolitons "quasibreathers".

KW - Breathers

KW - Freak waves

KW - Nonlinear Schrödinger equation

KW - Singularities

KW - Solitons

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Quasibreathers in the MMT model

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Keywords

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