  In this paper we study the soliton dynamics of a high-density Bose-Einstein
condensate (BEC) subject to a time-oscillating trap. The behavior of the BEC is
described with a modified Gross-Pitaevskii equation (mGPE) which takes into
account three-body losses, atomic feeding and quantum fluctuations (up to a
novel high-density term). A variational approximation (VA) is used to study the
behavior of a Gaussian pulse in a static double-well potential. Direct
numerical solutions of the mGPE corroborate that the center of the pulse
exhibits an oscillatory behavior (as the VA predicts), and show a novel
phenomenon of fragmentation and regeneration (FR). It is shown that this FR
process is destroyed if we consider a potential with a time-dependent quadratic
term, but the FR survives if the time dependence is introduced in a cubic term.
Comparison between the VA and the numerical solution revealed an excellent
agreement when the oscillations of the pulse remain in one of the potential
wells. The effects of the quantum fluctuating terms on the FR process are
studied. Finally, variational results using a supergaussian trial function are
obtained.
