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 derived straightforwardly. The combined effects of weak nonlinearity, dispersion and random irregularities lead to a nonlinear Schroödinger 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.

© 2002 The Royal Society