TRANSMISSION OF SOLITONS THROUGH RANDOM-MEDIA

The one-dimensional nonlinear Schrodinger (NLS) equation with a random potential function is used to model pulses in very long low dispersion optical fiber with random fluctuations. When the initial pulse is a soliton solution of the unperturbed NLS equation, we show that an approximate theory can be developed for the effects of the fluctuations by using an equivalent particle method. Results of direct numerical simulations are presented. Comparisons of the approximate theory and the direct numerical solutions indicate that the theory is accurate enough to use for finding statistics about the transmission of the soliton-like pulses through the fluctuations. Computations provide evidence for the existence of nonlinear localization, though with a large localization length.