Sound propagation in a cylindrical Bose-condensed gas

We study the normal modes of a cylindrical Bose condensate at $T=0\mathrm{}$ 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 $c=\sqrt{g\mathrm{n̄}/m},$ where $\mathrm{n̄}$ is the average density of the condensate over its cross-sectional area.