Localization of nonlinear dispersive waves in weakly random
media
By multiple scale expansions we show that the envelope
equation for the propagation of slowly modulated waves in random
media can be straightforwardly derived. The combined effects of
weak nonlinearity, dispersion and random irregularities lead to a
nonlinear Schr\"odinger equation with a complex damping term.
Analytical and numerical results are presented. Both analytical and
numerical solutions are discussed to examine the effects of
randomness on this simple yet typical weakly nonlinear dispersive
wave.