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

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