The first part of the talk will be devoted to recall the definition and classical results about scattering theory for the solutions to the nonlinear Schroedinger equation.

We shall see that the strength of nonlinearity plays a crucial role. Then we shall focus in the specific regime of mass-subcritical and short-range nonlinearity. In this context we shall see an extension of the classical result by Yajima-Tsutsumi, in particular we up-grade from L^2 to H^1 scattering. We shall also discuss some partial results concerning the scattering of second order moments, and I will mention some quite natural open questions.

 

This is a joint work with V. Georgiev.