Effects of three-body interaction on collective excitation and stability of Bose--Einstein condensate

This paper investigates the collective excitation and stability oflow-dimensional Bose--Einstein condensates with two- and three-bodyinteractions by the variational analysis of the time-dependentGross--Pitaevskii--Ginzburg equation. The spectrum of the low-energyexcitation and the effective potential for the width of thecondensate are obtained. The results show that: (i) the repulsivetwo-body interaction among atoms makes the frequency red-shifted forthe internal excitation and the repulsive or attractive three-bodyinteraction always makes it blue-shifted; (ii) the region for theexistence of the stable bound states is obtained by identifying thecritical value of the two- and three-body interactions.