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A trajectory approach is taken to the hydrodynamical treatment of collectiveexcitations of a Bose-Einstein condensate in a harmonic trap. The excitationsinduced by linear deformations of the trap are shown to constitute a broadclass of solutions that can be fully described by a simple nonlinear matrixequation. An exact closed-form expression is obtained for the solutiondescribing the mode {n=0, m=2} in a cylindrically symmetric trap, and thecalculated amplitude-dependent frequency shift shows good agreement with theexperimental results of the JILA group.Comment: RevTex, 4 pages, 1 eps figure, identical to the published versio

Closed class of hydrodynamical solutions for the collective excitations of a Bose-Einstein condensate