  We consider the nonlinear Schroedinger equation in higher dimension with
Dirichlet boundary conditions and with a non-local smoothing nonlinearity. We
prove the existence of small amplitude periodic solutions. In the fully
resonant case we find solutions which at leading order are wave packets, in the
sense that they continue linear solutions with an arbitrarily large number of
resonant modes. The main difficulty in the proof consists in solving a "small
divisor problem" which we do by using a renormalisation group approach.
