Wave turbulence in one-dimensional models

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

Research output: Contribution to journalArticlepeer-review

61 Scopus citations


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
StatePublished - May 15 2001
Externally publishedYes


  • 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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