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Random Wave Closures
Author(s) -
Benney D. J.,
Newell Alan C.
Publication year - 1969
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm196948129
Subject(s) - mathematics , zeroth law of thermodynamics , cumulant , closure (psychology) , mathematical analysis , sequence (biology) , dimension (graph theory) , spectrum (functional analysis) , statistical physics , order (exchange) , pure mathematics , physics , quantum mechanics , statistics , finance , biology , economics , market economy , genetics
A 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 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.