Generation of dispersive shock waves by the flow of a Bose-Einstein   condensate past a narrow obstacle
  We study the flow of a quasi-one-dimensional Bose-Einstein condensate incident onto a narrow obstacle. We consider a configuration in which a dispersive shock is formed and propagates upstream away from the obstacle while the downstream flow reaches a supersonic velocity, generating a sonic horizon. Conditions for obtaining this regime are explicitly derived and the accuracy of our analytical results is confirmed by numerical simulations. 
A. M. Kamchatnov and N. Pavloff
cond-mat.quant-gas nlin.PS