Discretization of Zakharov's equation
In Zakharov's equation the spectral function represent the entire
horizontal plane. In practical application one often has to use a
finite number of Fourier-modes that are determined for limited
regions of the horizontal plane, but vary from region to region. In
this note the Zakharov equation is carefully discretisized, and the
relationship between the spectral function over the entire
wave-number plane and the discrete Fourier-modes is established.
The applicability of some special cases of the discretisized
Zakharov equation is discussed.