Resonances in a trapped 3D Bose-Einstein condensate under periodically   varying atomic scattering length
  Nonlinear oscillations of a 3D radial symmetric Bose-Einstein condensate under periodic variation in time of the atomic scattering length have been studied analytically and numerically. The time-dependent variational approach is used for the analysis of the characteristics of nonlinear resonances in the oscillations of the condensate. The bistability in oscillations of the BEC width is invistigated. The dependence of the BEC collapse threshold on the drive amplitude and parameters of the condensate and trap is found. Predictions of the theory are confirmed by numerical simulations of the full Gross-Pitaevski equation. 
Fatkhulla Kh. Abdullaev, Ravil M. Galimzyanov, Marijana Brtka and   Roberto A. Kraenkel