A quasi-local Gross-Pitaevskii equation for attractive Bose-Einstein condensates

We study a quasi-local approximation for a nonlocal nonlinear Schrodinger equation. The problem is closely related to several applications, in particular to Bose-Einstein condensates with attractive two-body interactions. The nonlocality is approximated by a nonlinear dispersion term, which is controlled by physically meaningful parameters. We show that the phenomenology found in the nonlocal model is very similar to that present in the reduced one with the nonlinear dispersion. We prove rigorously the absence of collapse in the model, and obtain numerically its stable soliton-like ground state. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.