BEC From a Time-Dependent Variational Point of View
  We use the time-dependent variational of Balian and Veneroni to derive a set of equations governing the dynamics of a trapped Bose gas at finite temperature. We show that this dynamics generalizes the Gross-Pitaevskii equations in that it introduces a consistent coupling between the evolution of the condensate density, the thermal cloud and the anomalous density. 
M. Benarous