Enhanced localization of waves in one-dimensional random media due to nonlinearity: Fixed input case

Abstract

We study the influence of nonlinearity on wave localization in one-dimensional random media. Using a discrete nonlinear Schrodinger equation with a random on-site energy term, we calculate the localization length in a numerically exact manner. Unlike in many previous works, we fix the intensity of the incident wave and calculate quantities as a function of other parameters. We find that localization is enhanced due to nonlinearity for the focusing and defocusing nonlinearities. For small nonlinearity, the localization length is a decreasing function of nonlinearity. For sufficiently large nonlinearity, however, the localization length is found to approach a saturation value. (C) 2011 Elsevier B.V. All rights reserved