Of particular interest are one-mode densities which can be conveniently obtained using a one-amplitude generating function

For the one-point moments of the amplitude we have

where and subscript means differentiation with respect to times.

The first of these moments, , is the waveaction spectrum. Higher moments measure fluctuations of the waveaction -space distributions about their mean values [22]. In particular the r.m.s. value of these fluctuations is

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