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