Weakly nonlinear surface waves over a random seabed

We study the effects of multiple scattering of slowly modulated water waves by a weakly random bathymetry. The combined effects of weak nonlinearity, dispersion and random irregularities are treated together to yield a nonlinear Schr?dinger equation with a complex damping term. Implications for localization and side-band instability are discussed. Transmission and nonlinear evolution of a wave packet past a finite strip of disorder is examined.