Perturbation of non-ground stationary states in atomic Bose-Einstein condensate

Summary form only given. We report the new properties of Bose-Einstein condensate (BEC) of atoms in a harmonic trap. In the mean-field limit and s-scattering approximation the stationary states and dynamics BEC is described by the stationary and non-stationary Gross-Pitaevskii (GP) equations which contain cubic nonlinear term due to interatomic interaction. For a weakly perturbed stationary state corresponding to small oscillations of the order parameter around the stationary-state value, the linearized GP equation is reduced to the simultaneous Bogoliubov equations, which describe collective modes of BEC.