N = ∫ N ( k ) dk
E = ∫ ω( k ) N (k ) dk
(3)
K = ∫ k N ( k ) dk
Actually, only N is a real constant of motion. The energy E and the momentum K are only "formal" integral of
motion, "leaking" in the area of very large wave numbers. The high frequency truncation of the Hasselmann equation
leads to a leakage of the wave energy and momentum to a high frequency range, whereas the wave action flux is
mainly directed to a low frequency range. It can be presented as follows:
dK
dN
dE
= 0;
=  P;
= M ;
(4)
dt
dt
dt
Preservation of energy and momentum fluxes to high wave numbers is due to formation of weak turbulent
Kolmogorov spectra. The main theoretical point of the kinetic equation (1) is a description of the stationary equation
solution of :
Gnl ≡ 0
(5)
The simplest Kolmogorov weak turbulent stationary solution of the equation (1) was obtained in 1966 (Zakharov and

Filonenko, 1966):
g 4 3 P1 3
S (ω) =α 0
(6)
ω4
S (ω) is the energy spectrum defined by the relation:
where
2ω
S (ω ) dω dβ = ω (k ) N ( k ) dk =
N (ω, β ) dω dβ
(7)
2
g
In general terms the Kolmogorov spectra are anisotropic:
g 4 3 P1 3 g M
F
, β
S (ω, β) =
(8)
ωP
ω4
where F = F (ξ, β) is a function of two variables.
A solution (9) averaged over the angles is very close to energy frequency spectra, obtained in many laboratory and
field experiments (Toba 1972; Donelan et al. 1985).
Now, a question arises, how can t he exact Kolmogorov solution of the stationary equation (5) approximate solutions
of the nonstationary equation (1), especially in cases of applying forcing and damping sources? It should be noted
that for the first time an attempt to give an answer to this question is undertaken in paper (Komen, Hasselmann and
Hasselmann,1984). They show that even in the presence of input and dissipation there is the spectrum solution
S ~ 1 ω4 . The nonlinear flux is found out to be generally rather strong, so t hat relatively small deviations from the
4
solution S ~ 1 ω are sufficient to generate divergent fluxes, which can balance nonzero input and dissipation
source function in the cascade region (Komen et al.,1994). Unfortunately, at that time it was difficult to get an exact
estimation of basic parameters of problem solution.. A stationary solution obtained by solving nonstationary equation