  We study the equilibrium dynamics of a weakly interacting Bose-Einstein
condensate trapped in a box. In our approach we use a semiclassical
approximation 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
appropriate 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
miliseconds the system exhibits relaxation - reaches an equilibrium with
populations of different eigenstates fluctuating around their mean values.
