Asymptotic Behavior of the Nonlinear Schrr Odinger Equation with Rapidly-varying, Mean-zero Dispersion

In this paper we consider the nonlinear Schrr odinger equation with an oscillatory, mean-zero dispersion, which has recently been proposed as an alternative method of dispersion compensation for pulse transmission in optical bers. Under the assumption that the time scale on which the dispersion changes is short in comparison with the dispersion and nonlinearity time scales, we are able to factor out the leading order contribution of the dispersion which leads to an eeective equation for the pulse dynamics. This eeective equation is a nonlinear diiusion equation, which is shown by an amplitude-phase decomposition to reduce to the well known porous medium equation for the amplitude dynamics and a linear, nonconstant coeecient diiusion equation for the phase which is driven by the amplitude.