  The dynamics of a dark soliton in an elongated Bose-Einstein condensate at
finite temperatures is studied using numerical simulations. We find that in the
presence of harmonic confinement the soliton may oscillate even at finite
temperatures, but with an amplitude that increases with time, indicating the
decay of the soliton. The timescale of this decay decreases both with
increasing temperature and with increasing initial soliton velocity.
Simulations performed for the experiment of S. Burger et al., Phys. Rev. Lett.
83, 5198 (1999), reveal excellent agreement with the observed soliton decay,
confirming the crucial role of the thermal cloud in soliton dynamics.
