  We consider the dynamics of a dark soliton in an elongated harmonically
trapped Bose-Einstein condensate. A central question concerns the behavior at
finite temperatures, where dissipation arises due to the presence of a thermal
cloud. We study this problem using coupled Gross-Pitaevskii and $N$-body
simulations, which include the mean field coupling between the condensate and
thermal cloud. We find that the soliton decays relatively quickly even at very
low temperatures, with the decay rate increasing with rising temperature.
