## Oscillation frequencies as a function of the parameter *P* > 0 with *G* = −0.03, 0, 0.03 with lambda _{z}=sqrt{8}

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**Figure 8.** Oscillation frequencies as a function of the parameter *P* > 0 with *G* = −0.03, 0, 0.03 with \lambda _{z}=\sqrt{8}. The labels on the curves refer to different oscillation modes (see text and figure 7).

**Abstract**

We take into account the higher-order corrections in two-body scattering interactions within a mean-field description, and investigate the stability conditions and collective excitations of a harmonically trapped Bose–Einstein condensate (BEC). Our results show that the presence of higher-order corrections causes drastic changes to the stability condition of a BEC. In particular, we predict that with the help of the higher-order interaction, a BEC can now collapse even for positive scattering lengths; whereas, a usually unstable BEC with a negative scattering length can be stabilized by positive higher-order effects. The low-lying collective excitations are significantly modified as well, compared to those without the higher-order corrections. The conditions for a possible experimental scenario are also proposed.