  The dynamics of a two-component dilute Bose gas of atoms at zero temperature
is described in the mean field approximation by a two-component
Gross-Pitaevskii Equation. We solve this equation assuming a Gaussian shape for
the wavefunction, where the free parameters of the trial wavefunction are
determined using a moment method. We derive equilibrium states and the phase
diagrams for the stability for positive and negative s-wave scattering lengths,
and obtain the low energy excitation frequencies corresponding to the
collective motion of the two Bose condensates.
