# The Periodically Perturbed Nonlinear Schrodinger Equation

And Its Applications to Fiber Optic Communications

## J. Nathan Kutz (Princeton University)

This talk considers the stability of both soliton-like
and non-soliton pulses in nonlinear optical fibers
where the governing equation is the periodically
perturbed nonlinear Schrodinger equation. In particular,
an overview of various communications systems is
given with emphasis being placed on the dispersion
managed nonlinear Schrodinger equation, i.e., the
case where the sign of the dispersion changes periodically
as a pulse propagates. Here, Floquet theory is
used to describe the stability of plane waves which
correspond to constant amplitude signals (0's and 1's)
and the properties of the Green's function associated
with the linear problem is used to describe pulse
deformations. The main results include a derivation of the
leading order behavior as well as an estimate on
the lengthscale of validity.