Dynamics of Coupled Topological - Collective Modes of a Bose-Einstein Condensate

We develop the theory of the resonant formation of coupled topological-collective coherent modes in the presence of a quantized trap and classical external field. The coupling between the topological and the collective modes can be linear as well as non-linear depending upon the tuning of the external extremely low frequency electromagnetic field. This tuning depends on the trap frequency and the energy level separation between the ground and the first excited topological coherent mode modified by the two body atomic collisions.