Transmission of Solitons through Random Media

Robert Knapp
rknapp@wri.com

The one-dimensional nonlinear Schr\"odinger (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.