Many-body approach to low-lying collective excitations in a BEC   approaching collapse
  An approximate many-body theory incorporating two-body correlations has been employed to calculate low-lying collective multipole frequencies in a Bose-Einstein condensate containing $A$ bosons, for different values of the interaction parameter $\lambda=\frac{Aa_{s}}{a_{ho}}$. Significant difference from the variational estimate of the Gross-Pitaevskii equation has been found near the collapse region. This is attributed to two-body correlations and finite range attraction of the realistic interatomic interaction. A large deviation from the hydrodynamic model is also seen for the second monopole breathing mode and the quadrupole mode for large positive $\lambda$. 
Anindya Biswas and Tapan Kumar Das