Bright and Dark Solitons and Breathers in Strongly Repulsive   Bose-Einstein Condensates
  Collisional dynamics of solitary matter waves of superfluid hard core bosons, consisting of dark and bright non-linear waves as well as supersonic periodic trains, reveals remarkable richness and coherence, with the phase of the condensate playing a key role. Depending upon the condensate density and their relative velocity, two distinctive collisional types emerge: the intuitively expected repulsive collisions due to the hard core boson constraint; and, also collisions in which they "pass through" one another. In addition to confirming the soliton status of both bright and dark solitary waves, our studies reveal a variety of multi-solitons including multiple families of breathers, that can be produced and precisely controlled via quantum phase engineering. 
William P. Reinhardt, Indubala I. Satija, Bryce Robbins and Charles W.   Clark
quant-ph