  Symmetry breaking during phase transitions can lead to the formation of
topological defects (such as vortex lines in superfluids). However, the usually
studied BEC's have the shape of a cigar, a geometry that impedes vortex
formation, survival, and detection. I show that, in elongated traps, one can
expect the formation of "grey solitons" (long-lived, non-topological "phase
defects") as a result of the same mechanism. Their number will rise
approximately in proportion to the transition rate. This steep rise is due to
the increasing size of the region of the BEC cigar where the phase of the
condensate wavefunction is chosen locally (rather than passed on from the
already formed BEC).
