Scattering properties of envelope solitons in disordered systems: decay of localization effects by strong nonlinearity

Abstract

We study the scattering of nonlinear wavepackets in the form of envelope soli tons by a one-dimensional disordered system. We briefly review the features of the scattering for linear waves and obtain some results for linear wave packets to demonstrate their common exponential decay of the transmission coefficient, characterized by a localization length. We consider the same process for envelope solitons, and we show in the framework of the simplest model, that, above a certain threshold, strong non linearity allows undistorted propagation of these wavepackets. We describe how this behaviour can be obtained, for the nonlinear Schriidinger equation, by means of a simple independent scattering approach, using results of soliton perturbation theory to compute one-impurity reflection coefficients in the Born approximation. We derive equations to describe the transmission of the soli ton parameters and we analyse them in full detail. The main result of our study is the conclusion that a strong nonlinearity stipulates two spatial scales in the wavepacket scattering by disordered systems. The first spatial scale depends on the amplitude and it may be very large, and the second one is the usual localization length. As a consequence the non linear wavepackets or solitons are much more stable against disorder than linear ones.