Dysthe, K.B. ( 1979). “Note on a modification of the nonlinear Schrodinger equation for application to deep water wave,” Proc. R. Soc. London A, 369, 105–114.

Stansberg, C.T. and Gudmestad, O.T. ( 1996). “Nonlinear random wave kinematics models verified against measurements in steep waves,” Proc. OMAE 96, Firenze, June 1996.

According to the theoretical work of Alber (1978), the self-modulational instability disappears when the spectral bandwidth (σ) exceeds a critical value that is proportional to the mean square slope His stability criterion seems to be satisfied in most sea conditions. The absence of the self-modulation instability does not mean that nonlinear interactions are unimportant.

In the spectral regime, they are at least partly responsible for the downshift of the spectral peak. That is a slow statistical effect described by the Hasselman type interaction integral. Only when the spectral bandwidth is small (subcritical in Alber's sense) can a rapid downshift take place, as demonstrated by us.

In the spatial regime, the nonlinear interaction may have unexpected effects yet to be explored.

Alber, I.E. ( 1978). “The effects of randomness on the stability of two-dimensional surface wavetrains,” Proc. R. Soc. Lond. A, 363, pp. 525–546.