Sound propagation in a cylindrical Bose-condensed gas

We study the normal modes of a cylindrical Bose condensate at $T = 0$ using the linearized time-dependent Gross-Pitaevskii equation in the Thomas-Fermi limit. These modes are relevant to the recent observation of pulse propagation in long, cigar-shaped traps. We find that pulses generated in a cylindrical condensate propagate with little spread at a speed $c = \sqrt{g\bar n /m}$, where $\bar n$ is the average density of the condensate over its cross-sectional area.