We study the equilibrium dynamics of a weakly interacting Bose-Einstein con
densate tapped in a box. In our approach we use a semiclassical approximati
on similar to the description of a multi-mode laser. In dynamical equations
derived from a full N-body quantum Hamiltonian we substitute all creation
(and annihilation) operators (of a particle in a given box state) by approp
riate c-number amplitudes. The set of nonlinear equations obtained in this
way is solved numerically. We show that on the time scale of a few miliseco
nds the system exhibits relaxation - reaches an equilibrium with population
s of different eigenstates fluctuating around their mean values. (C) 2001 O
ptical Society of America.