  We assume the macroscopic wave function of a Bose-Einstein condensate as a
superposition of Gaussian wave packets, with time-dependent complex width
parameters, insert it into the mean-field energy functional corresponding to
the Gross-Pitaevskii equation (GPE) and apply the time-dependent variational
principle. In this way the GPE is mapped onto a system of coupled equations of
motion for the complex width parameters, which can be analyzed using the
methods of nonlinear dynamics. We perform a stability analysis of the fixed
points of the nonlinear system, and demonstrate that the eigenvalues of the
Jacobian reproduce the low-lying quantum mechanical Bogoliubov excitation
spectrum of a condensate in an axisymmetric trap.
