Search

Beyond the mean-field theory, a new model of the Gross-Pitaevskii equation (GPE) that describes the dynamics of Bose-Einstein condensates (BECs) is derived using an appropriate phase-imprint on the old wavefunction. This modified version of the GPE in addition to the two-body interactions term, also takes into account effects of the three-body interactions. The three-body interactions consist of a quintic term and the delayed nonlinear response of the condensate system term. Then, the modulational instability (MI) of the new GPE confined in an attractive harmonic potential is investigated. The analytical study shows that the three-body interactions destabilize more the condensate system while the external potential alleviates the instability. Numerical results confirm the theoretical predictions. Further numerical investigations of the behavior of solitons reveal that the three-body interactions enhance the appearance of solitons, increase the number of solitons generated and deeply change the lifetime of solitons. Moreover, the external potential delays the appearance of solitons. Besides, a new initial condition is introduced which enables to increase the number of solitons created and deeply affects the trail of chains of solitons generated. Moreover, the MI of a condensate without the external potential, and in a repulsive potential is also investigated. [ABSTRACT FROM AUTHOR]

The modulational instability (MI) of Bose-Einstein condensates based on a modified Gross-Pitaevskii equation (GPE) which takes into account quantum fluctuations and a shape-dependent term, trapped in an external time-dependent complex potential is investigated. The external potential consists of an expulsive parabolic background with a complex potential and a gravitational field. The theoretical analysis uses a modified lens-type transformation which converts the modified GPE into a modified form without an explicit spatial dependence. A MI criterion and a growth rate are explicitly derived, both taking into account quantum fluctuations and the parameter related to the feeding or loss of atoms in the condensate which significantly affect the gain of instability of the condensate. Direct numerical simulations of the modified GPE show convincing agreements with analytical predictions. In addition, our numerical results also reveal that the gravitational field has three effects on the MI: (i) the deviation backward or forward of solitons trains, (ii) the enhancement of the appearance of the MI and (iii) the reduction of the lifetime of pulses. Moreover, numerical simulations proved that it is possible to control the propagation of the generated solitons trains by a proper choice of parameters characterizing both the loss or feeding of atoms and the gravitational field, respectively. [ABSTRACT FROM AUTHOR]