Dispersive Estimates for the Schrodinger Equation

Abstract

Finally in Chapter 3 we consider a problem involving the non-linear Schrodinger equation. In particular, we consider the following equation that arises in fiber optic communication systems, iut+dtu xx+u2u=0. We can reduce this to a non-linear, non-local eigenvalue equation that describes the so-called dispersion management solitons. We prove that the dispersion management solitons decay exponentially in x and in the Fourier transform of x.