ASYMPTOTIC-BEHAVIOR OF THE NONLINEAR SCHRODINGER-EQUATION WITH RAPIDLY VARYING, MEAN-ZERO DISPERSION

In this paper we consider the nonlinear Schrodinger equation with an o scillatory, mean-zero dispersion, which has recently been proposed as an alternative method of dispersion compensation for pulse transmissio n in optical fibers, 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 effective equation f or the pulse dynamics. This effective equation is a nonlinear diffusio n equation, which is shown by an amplitude-phase decomposition to redu ce to the well-known porous medium equation for the amplitude dynamics and a linear, nonconstant coefficient diffusion equation for the phas e which is driven by the amplitude.