  Starting from coupled Gross-Pitaevskii equation (GPE) describing the dynamics
of binary Bose Einstein Condensate (BEC), we have explored the dynamics of the
width of initial wave-packets by following two different approaches. We have
followed a recent coherent state based approach and have shown that in binary
BEC the oscillation of the width of the wave packet can give rise to
instability at a certain condition. Alternately we have proceeded by
considering the trial ground state solutions for both the species and through
the Ehrenfest theorem shown the existence of an instability which may lead to
phase separation of the two species.
