Bogoliubov and Mitropolsky theory in the realm of ultracold quantum gases

الملخص EN

The present paper addresses the topical issue of collective modesin ultracold quantum gases.

At first, we discuss the effects of the modulation interaction for a positive s-wave scattering length in order to study the resonance curve which has been observed in the experiment.

Furthermore, we use a variational Gaussian ansatz for a spherical-symmetric trap and obtain the corresponding equation of motion for the condensate width in order to revisit the problem of the modulation interaction and prominent nonlinear effects, including resonance in the collective mode frequency.