RANDOM WAVE CLOSURES

DJ BENNEY DJ, Alan C Newell

Research output: Contribution to journalArticle

108 Citations (Scopus)

Abstract

Detailed study is made of the way in which weak nonlinearities affect the statistical properties of a system of dispersive waves. Given that at some initial instant the spectral cumulants are sufficiently smooth it is shown that they will remain smooth to a zeroth order, save in one dimension where a discrete spectrum may eventually be generated. Of prime interest is the fact that on considering the long time behavior of the system, one is led to a sequence of closures for the zeroth order spectral functions. Apparent difficulties associated with the irretraceability of the solution are discussed. The structure of the closure equations depends on the asymptotic behavior of a class of singular integrals.

Original languageEnglish (US)
Pages (from-to)29-53
Number of pages25
JournalStudies in Applied Mathematics
Volume48
Issue number1
StatePublished - Mar 1969
Externally publishedYes

Fingerprint

Zeroth
Closure
Spectral Function
Discrete Spectrum
Singular Integrals
Cumulants
Long-time Behavior
Instant
Statistical property
One Dimension
Asymptotic Behavior
Nonlinearity
Class

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

RANDOM WAVE CLOSURES. / BENNEY DJ, DJ; Newell, Alan C.

In: Studies in Applied Mathematics, Vol. 48, No. 1, 03.1969, p. 29-53.

Research output: Contribution to journalArticle

BENNEY DJ, DJ & Newell, AC 1969, 'RANDOM WAVE CLOSURES', Studies in Applied Mathematics, vol. 48, no. 1, pp. 29-53.
BENNEY DJ, DJ ; Newell, Alan C. / RANDOM WAVE CLOSURES. In: Studies in Applied Mathematics. 1969 ; Vol. 48, No. 1. pp. 29-53.
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