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On the energy transfer equation for weakly interacting waves. (English) Zbl 0546.73026
(From author’s summary.) The transfer equation based on analysis of the equations for spectral semi-invariant, while not invoking the equations for realization of the random wave field, are derived. Uniformly valid asymptotic expansions for the third and fourth spectral semi-invariant are constructed using the multiple scale method and the matched asymptotic expansion method. This makes it possible to investigate the boundary layer in a neighborhood of the resonant surface where intensive growth in time of the third spectral semi-invariant occurs. This boundary layer defines the form of the transfer equations. An analogous boundary layer for the fourth spectral semi-invariant and its influence on the second and the third spectral semi-invariant are also investigated.
Reviewer: W.Ames

MSC:
74J99 Waves in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
74H50 Random vibrations in dynamical problems in solid mechanics
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