## Equilibrium widths *v*_{z} (a) and *v* (b) come from equations (15) and (15) as a function of |*P*| for *G* = 0.03, 0 and −0.03 respectively in the case of cylindrical symmetry of λ_{z} = 2

_{z}

#### figure

Figures are generally photos, graphs and static images that would be represented in traditional pdf publications.

**Figure 10.** Equilibrium widths *v _{z}* (a) and

*v*(b) come from equations (15) and (15) as a function of |

*P*| for

*G*= 0.03, 0 and −0.03 respectively in the case of cylindrical symmetry of λ

_{z}= 2.

**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.