Discretization of Zakharov's equation

In Zakhafov's equation the spectral function represents the entire horizont al plane. In practical applications one often has to use a finite number of Fourier-modes that are determined for limited regions of the horizontal pl ane, but vary from region to region. In this note the Zakharov equation is carefully discretized, and the relationship between the spectral function o ver the entire wave-number plane and the discrete Fourier-modes is establis hed. The applicability of some special cases of the discretized Zakharov eq uation is discussed. (C) Elsevier, Paris.