Formation of fundamental structures in Bose-Einstein condensates

The mean-field interaction in a Bose condensate provides a nonlinearity which can allow stable structures to exist in the mean-field wavefunction. We discuss a number of examples where condensates, modelled by the one-dimensional Gross-Pitaevskii equation, can produce grey solitons and we consider in detail the case of two identical condensates colliding in a harmonic trap. Solitons are shown to form from dark interference fringes when the soliton structure, constrained in a defined manner, has lower energy than the interference fringe and an analytic expression is given for this condition. (author). Letter-to-the-editor