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A novel discrete model (D-model) is presented describing nonlinear waveinteractions in systems with small and moderate nonlinearity under narrowfrequency band excitation. It integrates in a single theoretical frame twomechanisms of energy transport between modes, namely intermittency and energycascade and gives conditions when which regime will take place. Conditions forthe formation of a cascade, cascade direction, conditions for cascadetermination, etc. are given and depend strongly on the choice of excitationparameters. The energy spectra of a cascade may be computed yielding discreteand continuous energy spectra. The model does not need statistical assumptionsas all effects are derived from the interaction of distinct modes. In theexample given -- surface water waves with dispersion function $\o^2=g\,k$ andsmall nonlinearity -- D-model predicts asymmetrical growth of side-bands forBenjamin-Feir instability while transition from discrete to continuous energyspectrum excitation parameters properly chosen yields the saturated Phillips'power spectrum $\sim g^2\o^{-5}$. D-model can be applied to the experimentaland theoretical study of numerous wave systems appearing in hydrodynamics,nonlinear optics, electrodynamics, plasma, convection theory, etc.

Energy transport in weakly nonlinear wave systems with narrow frequency band excitation