  We study the dynamics of two interacting Bose-Einstein condensates, by
numerically solving two coupled Gross-Pitaevskii equations at zero temperature.
We consider the case of a sudden transfer of atoms between two trapped states
with different magnetic moments: the two condensates are initially created with
the same density profile, but are trapped into different magnetic potentials,
whose minima are vertically displaced by a distance much larger than the
initial size of both condensates. Then the two condensates begin to perform
collective oscillations, undergoing a complex evolution, characterized by
collisions between the two condensates. We investigate the effects of their
mutual interaction on the center-of-mass oscillations and on the time evolution
of the aspect ratios. Our theoretical analysis provides a useful insight into
the recent experimental observations by Maddaloni et al., cond-mat/0003402.
