| Abstract
| - In this letter we present a new method, called increment chain equation method (ICEM), for computing a cascade of distinct modes in a two-dimensional weakly nonlinear wave system generated by narrow frequency band excitation. The ICEM is a means for computing the quantized energy spectrum as an explicit function of frequency ω 0 and stationary amplitude A0 of excitation. The physical mechanism behind the generation of the quantized cascade is modulation instability. The ICEM can be used in numerous 2D weakly nonlinear wave systems with narrow frequency band excitation appearing in hydrodynamics, nonlinear optics, electrodynamics, convection theory etc. In this letter the ICEM is demonstrated with examples of gravity and capillary waves with dispersion functions ω( k)∼ k1/2 and ω( k)∼ k3/2, respectively, and for two different levels of nonlinearity ε= A0k0: small (ε∼0.1 to 0.25) and moderate (ε∼0.25 to 0.4).
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