Stability analysis of the D-dimensional nonlinear Schrodinger equation with trap and two- and three-body interactions

Considering the static solutions of the D-dimensional nonlinear Schrodinger equation with trap and attractive two-body interactions, the existence of stable solutions is limited to a maximum critical number of particles, when D greater than or equal to 2. In case D = 2, we compare the variational ap proach with the exact numerical calculations. We show that, the addition of a positive three-body interaction allows stable solutions beyond the criti cal number. In this case, we also introduce a dynamical analysis of the con ditions for the collapse. (C) 2000 Published by Elsevier Science B.V. All r ights reserved.