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

Abstract 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 ≥2. In case D =2, we compare the variational approach with the exact numerical calculations. We show that, the addition of a positive three-body interaction allows stable solutions beyond the critical number. In this case, we also introduce a dynamical analysis of the conditions for the collapse.