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On the Bifurcation of a Random Spectrum of Weakly Nonlinear Deep‐Water Gravity Waves
Author(s) -
Ma YanChow
Publication year - 1982
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/sapm1982662145
Subject(s) - bifurcation , spectrum (functional analysis) , nonlinear system , wavenumber , essential spectrum , bandwidth (computing) , physics , bifurcation theory , modulational instability , mathematics , homogeneous , mathematical analysis , classical mechanics , frequency spectrum , statistical physics , spectral density , quantum mechanics , telecommunications , computer science , statistics
The bifurcation of a narrow‐band homogeneous random spectrum of deep‐water gravity waves into an inhomogeneous random spectrum is studied under the assumption of weak nonlinearity. The modulational wavenumber for the bifurcation depends on the characteristic bandwidth of the spectrum as well as on the energy of the spectrum. The stability of the bifurcated spectrum is examined.