Note on modified Zakharov’s equation accounting for scattering in disordered media

We derive, for a simple nonlinear dispersive system, a modified Zakharov equation accounting for random scattering of broad-banded waves. The additional new term is linear in the frequency spectrum with a complex coefficient which is formally the same as that for narrow-banded waves. The nonlinear term representing four-wave resonant interaction is unchanged. Corresponding modification of Hasselman’s kinetic equation for the energy spectrum of random waves is also discussed. This suggests that treatment of the oceanographic problem for the algebraically more complex case of surface water waves is similarly straightforward, and should be useful to improve the numerical models of ocean surface waves.