  We show that quasi-one dimensional Bose-Einstein condensate under suitable
conditions can exhibit a Berezinskii-Kosterlitz-Thouless phase transition. The
role played by quantized vortices in two dimensional case, is played in this
case by dark solitons. We find that the critical temperature for this
transition lies in nano Kelvin range and below, for a wide range of
experimentally accessible parameters. It is seen that the high temperature
(disordered) phase differs from low temperature (ordered) phase in terms of
phase coherence, which can be used as an experimental signature for observing
this transition.
