We study the time-evolution of the two dimensional multi-component
Bose-Einstein condensate in an external harmonic trap with arbitrary
time-dependent frequency. We show analytically that the time-evolution of the
total mean-square radius of the wave-packet is determined in terms of the same
solvable equation as in the case of a single-component condensate. The dynamics
of the total mean-square radius is also the same for the rotating as well as
the non-rotating multi-component condensate. We determine the criteria for the
collapse of the condensate at a finite time. Generalizing our previous work on
a single-component condensate, we show explosion-implosion duality in the
multi-component condensate.Comment: Two-column 6 pages, RevTeX, no figures(v1); Added an important
reference, version to appear in Physical Review A (v2
