Wave turbulence in one-dimensional models

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

Research output: Contribution to journalArticle

50 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)573-619
Number of pages47
JournalPhysica D: Nonlinear Phenomena
Volume152-153
DOIs
StatePublished - May 15 2001

Fingerprint

One-dimensional Model
Turbulence
turbulence
nonlinearity
Nonlinearity
Dispersive Equations
Coherent Structures
One-dimensional System
Wave equations
wave equations
Discrepancy
Two Parameters
Wave equation
Numerical Results
Model

Keywords

  • Kinetic wave equation
  • Kolmogorov spectra
  • Quasisolitons
  • Wave collapses
  • Weak turbulence

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Wave turbulence in one-dimensional models. / Zakharov, Vladimir E; Guyenne, P.; Pushkarev, A. N.; Dias, F.

In: Physica D: Nonlinear Phenomena, Vol. 152-153, 15.05.2001, p. 573-619.

Research output: Contribution to journalArticle

Zakharov, Vladimir E ; Guyenne, P. ; Pushkarev, A. N. ; Dias, F. / Wave turbulence in one-dimensional models. In: Physica D: Nonlinear Phenomena. 2001 ; Vol. 152-153. pp. 573-619.
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