Nonstationary excitations in Bose-Einstein condensates under the action of periodically varying scattering length with time dependent frequencies

We investigate nonstationary excitations in 3D-Bose-Einstein condensates in a spherically symmetric trap potential under the modulation of scattering length with slowly varying frequencies (adiabatic modulation). By numerically solving the Gross-Pitaevskii equation we observe a step-wise increase in the amplitude of oscillation due to successive phase locking between driving frequency and nonlinear frequency. Such a nonstationary excitation has been shown to exist by an analytic approach using variational procedure and perturbation theory in the action-angle variables. By using a canonical perturbation theory, we have identified the successive resonance excitations whenever the driven frequency matches the nonlinear frequency or its subharmonics.