Closed class of hydrodynamical solutions for the collective excitations ofa Bose-Einstein condensate - art. no. 033604

A trajectory approach is taken to the hydrodynamical treatment of collectiv e excitations of a Bose-Einstein condensate in a harmonic trap. The excitat ions induced by linear deformations of the trap are shown to constitute a b road class of solutions that can be fully described by a simple nonlinear m atrix equation. An exact closed-form expression is obtained for the solutio n describing the mode {n=0, m=+2} in a cylindrically symmetric trap, and th e calculated amplitude-dependent frequency shift shows good agreement with the experimental results of the JILA group.