DJ BENNEY DJ, Alan C Newell

Research output: Contribution to journalArticle

108 Scopus citations


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
Issue number1
Publication statusPublished - Mar 1969
Externally publishedYes


ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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