Abstract
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 $c=\sqrt{g\mathrm{n\ifmmode \bar{}\else \={}\fi{}}/m},$ where $\mathrm{n\ifmmode \bar{}\else \={}\fi{}}$ is the average density of the condensate over its cross-sectional area.
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