FREQUENCY-SHIFT AND MODE-COUPLING IN THE NONLINEAR DYNAMICS OF A BOSE-CONDENSED GAS

We investigate the behavior of large amplitude oscillations of a trapp ed Bose-condensed gas of alkali-metal atoms at zero temperature, by so lving the equations of hydrodynamics for collective modes. Due to the atom-atom interaction, the equations of motion are nonlinear and give rise to significant frequency shift and mode coupling. We provide anal ytic expressions for the frequency shift, pointing out the crucial rol e played by the anisotropy of the confining potential. For special val ues of the anisotropy parameter the mode coupling is particularly stro ng and the frequency shift becomes large, revealing a peculiar behavio r of the Bose-condensed gas. Consequences on the theory of collapse an d revival of collective excitations are also discussed. [S1050-2947(97 )05012-9].