Wave turbulence in one-dimensional models

V. E. Zakharov; P. Guyenne; A. N. Pushkarev; F. Dias

doi:10.1016/S0167-2789(01)00194-4

Wave turbulence in one-dimensional models

V. E. Zakharov, P. Guyenne, A. N. Pushkarev, F. Dias

Mathematics

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

56 Scopus citations

Abstract

A two-parameter nonlinear dispersive wave equation proposed by Majda, McLaughlin and Tabak is studied analytically and numerically as a model for the study of wave turbulence in one-dimensional systems. Our ultimate goal is to test the validity of weak turbulence theory. Although weak turbulence theory is independent on the sign of the nonlinearity of the model, the numerical results show a strong dependence on the sign of the nonlinearity. A possible explanation for this discrepancy is the strong influence of coherent structures - wave collapses and quasisolitons - in wave turbulence.

Original language	English (US)
Pages (from-to)	573-619
Number of pages	47
Journal	Physica D: Nonlinear Phenomena
Volume	152-153
DOIs	https://doi.org/10.1016/S0167-2789(01)00194-4
State	Published - May 15 2001

Keywords

Kinetic wave equation
Kolmogorov spectra
Quasisolitons
Wave collapses
Weak turbulence

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/S0167-2789(01)00194-4

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@article{babefad641ac4a82aa8541c31f4aae80,

title = "Wave turbulence in one-dimensional models",

abstract = "A two-parameter nonlinear dispersive wave equation proposed by Majda, McLaughlin and Tabak is studied analytically and numerically as a model for the study of wave turbulence in one-dimensional systems. Our ultimate goal is to test the validity of weak turbulence theory. Although weak turbulence theory is independent on the sign of the nonlinearity of the model, the numerical results show a strong dependence on the sign of the nonlinearity. A possible explanation for this discrepancy is the strong influence of coherent structures - wave collapses and quasisolitons - in wave turbulence.",

keywords = "Kinetic wave equation, Kolmogorov spectra, Quasisolitons, Wave collapses, Weak turbulence",

author = "Zakharov, {V. E.} and P. Guyenne and Pushkarev, {A. N.} and F. Dias",

note = "Funding Information: The authors are grateful to D. McLaughlin, A. Majda, D. Cai and E. Tabak for useful discussions and for providing their results before publication. This work was performed in the framework of the NATO Linkage Grant OUTR.LG 970583. V. Zakharov and A. Pushkarev also acknowledge support of the US Army, under the grant DACA 39-99-C-0018, and of ONR, under the grant N00014-98-1-0439. F. Dias and P. Guyenne acknowledge support of DGA, under the contract ERS 981135. A. Pushkarev wishes to thank F. Dias for his hospitality during a visit to Nice in the fall of 1998.",

year = "2001",

month = may,

day = "15",

doi = "10.1016/S0167-2789(01)00194-4",

language = "English (US)",

volume = "152-153",

pages = "573--619",

journal = "Physica D: Nonlinear Phenomena",

issn = "0167-2789",

publisher = "Elsevier",

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TY - JOUR

T1 - Wave turbulence in one-dimensional models

AU - Zakharov, V. E.

AU - Guyenne, P.

AU - Pushkarev, A. N.

AU - Dias, F.

N1 - Funding Information: The authors are grateful to D. McLaughlin, A. Majda, D. Cai and E. Tabak for useful discussions and for providing their results before publication. This work was performed in the framework of the NATO Linkage Grant OUTR.LG 970583. V. Zakharov and A. Pushkarev also acknowledge support of the US Army, under the grant DACA 39-99-C-0018, and of ONR, under the grant N00014-98-1-0439. F. Dias and P. Guyenne acknowledge support of DGA, under the contract ERS 981135. A. Pushkarev wishes to thank F. Dias for his hospitality during a visit to Nice in the fall of 1998.

PY - 2001/5/15

Y1 - 2001/5/15

N2 - A two-parameter nonlinear dispersive wave equation proposed by Majda, McLaughlin and Tabak is studied analytically and numerically as a model for the study of wave turbulence in one-dimensional systems. Our ultimate goal is to test the validity of weak turbulence theory. Although weak turbulence theory is independent on the sign of the nonlinearity of the model, the numerical results show a strong dependence on the sign of the nonlinearity. A possible explanation for this discrepancy is the strong influence of coherent structures - wave collapses and quasisolitons - in wave turbulence.

AB - A two-parameter nonlinear dispersive wave equation proposed by Majda, McLaughlin and Tabak is studied analytically and numerically as a model for the study of wave turbulence in one-dimensional systems. Our ultimate goal is to test the validity of weak turbulence theory. Although weak turbulence theory is independent on the sign of the nonlinearity of the model, the numerical results show a strong dependence on the sign of the nonlinearity. A possible explanation for this discrepancy is the strong influence of coherent structures - wave collapses and quasisolitons - in wave turbulence.

KW - Kinetic wave equation

KW - Kolmogorov spectra

KW - Quasisolitons

KW - Wave collapses

KW - Weak turbulence

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U2 - 10.1016/S0167-2789(01)00194-4

DO - 10.1016/S0167-2789(01)00194-4

M3 - Article

AN - SCOPUS:0035873663

VL - 152-153

SP - 573

EP - 619

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

ER -

Wave turbulence in one-dimensional models

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Keywords

ASJC Scopus subject areas

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