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We derive Ehrenfest like equations for the coupled Gross Pitaevskii equations(CGPE) which describe the dynamics of the binary Bose-Einstein condensate(BBEC) both in the free particle regime and in the regime where condensate iswell trapped. Instead of traditional variational technique, we propose a newEhrenfest based approach to explore so far unrevealed dynamics for CGPE andillustrate the possibility of almost shape invariant states in both theregimes. In absence of trapping potential, when all the interactions present inthe system are attractive, it is possible for an initially mixed Gaussian stateto propagate with almost no change in width if the proper initial condition issatisfied. Even for repulsive intra-atomic and attractive inter-atomicinteraction ($g_{\alpha\beta}$) one can tune $|g_{\alpha\beta}|$ such that thewidth of the propagating wave packet remains bounded within almost about$10\%$. We also discuss the dynamics of the initially phase separatedcondensate and have shown the breakdown of Gaussian nature of the wave packetsdue to collisions. However, when BEC is trapped in simple harmonicoscillator(SHO) potential, for $g_{\alpha\beta}>0$, it is possible for aninitially overlapping state to retain its initial shape if $g_{\alpha\beta}$ isless than a critical value ($g_{\alpha\beta}^c$). If $g_{\alpha\beta}$ exceeds$g_{\alpha\beta}^c$, an overlapping state can become phase separated whilekeeping its shape unchanged.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Dynamics of binary Bose-Einstein condensate via Ehrenfest like equations: Appearance of almost shape invariant states