QUASI-ONE-DIMENSIONA1 CHARACTER OF SOUND-PROPAGATION IN ELONGATED BOSE-EINSTEIN CONDENSED CLOUDS

We show that under rather general conditions the propagation of sound pulses along the long axis of a Bose-Einstein condensed cloud in a ver y anisotropic trap is essentially one dimensional. In the linear regim e, we demonstrate that the square of the velocity of propagation is gi ven by the square of the local sound velocity c(2)=nU(0)/m averaged ov er the cross section of the cloud. We also carry out calculations-in t he nonlinear regime and determine how the speed of the pulse depends o n its amplitude. [S1050-2947(98)08608-9].