Stability analysis of the D-dimensional nonlinear Schroedinger equation   with trap and two- and three-body interactions
  Considering the static solutions of the D-dimensional nonlinear Schroedinger equation with trap and attractive two-body interactions, the existence of stable solutions is limited to a maximum critical number of particles, when D is greater or equal 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. 
A. Gammal, T. Frederico, Lauro Tomio, and F.Kh. Abdullaev