DYNAMICS OF BOSE-EINSTEIN CONDENSATES - VARIATIONAL SOLUTIONS OF THE GROSS-PITAEVSKII EQUATIONS

A variational technique is applied to solve the time-dependent nonline ar Schrodinger equation (Gross-Pitaevskii equation) with the goal to m odel the dynamics of dilute ultracold atom clouds in the Bose-Einstein condensed phase. We derive analytical predictions for the collapse, e quilibrium widths, and evolution laws of the condensate parameters and find them to be in very good agreement with our numerical simulations of the nonlinear Schrodinger equation. It is found that not only the number of particles, but also both the initial width of the condensate and the effect of different perturbations to the condensate may play a crucial role in the collapse dynamics. The results are applicable wh en the shape of the condensate is sufficiently simple.