Mean--Field and Nonlinear Dynamics in Many--Body Quantum Systems
  In this paper we discuss in detail the nonlinear equations of the mean--field approximation and their connection to the exact many--body Schr\"odinger equation. Then we analyze the mean--field approach and the nonlinear dynamics of a trapped condensate of weakly--interacting bosons. 
V.R. Manfredi and L. Salasnich