  We investigate the effect of anharmonicity and interactions on the dynamics
of an initially Gaussian wavepacket in a weakly anharmonic potential. We note
that depending on the strength and sign of interactions and anharmonicity, the
quantum state can be either localized or delocalized in the potential. We
formulate a classical model of this phenomenon and compare it to quantum
simulations done for a self consistent potential given by the Gross-Pitaevskii
Equation.
