Generation of oblique dark solitons in supersonic flow of Bose-Einstein condensate past an obstacle

Nonlinear and dispersive properties of Bose-Einstein condensate (BEC) provide a possibility of formation of various nonlinear structures such as vortices and bright and dark solitons (see, e.g., [1]). Yet another type of nonlinear wave patterns has been observed in a series of experiments on the BEC flow past macroscopic obstacles [2]. In [3] these structures have been associated with spatial dispersive shock waves. Spatial dispersive shock waves represent dispersive analogs of the the well-known viscous spatial shocks (oblique jumps of compression) occurring in supersonic flows of compressible fluids past obstacles. In a viscous fluid, the shock can be represented as a narrow region within which strong dissipation processes take place and the thermodynamic parameters of the flow undergo sharp change. On the contrary, if viscosity is negligibly small compared with dispersion effects, the shock discontinuity resolves into an expanding in space oscillatory structure which transforms gradually, as the distance from the obstacle increases, into a \fan" of stationary solitons. If the obstacle is small enough, then such a \fan" reduces to a single spatial dark soliton [4]. Here we shall present the theory of these new structures in BEC

Interaction of oblique dark solitons in two-dimensional supersonic nonlinear Schr\"odinger flow

We investigate the collision of two oblique dark solitons in the two dimensional supersonic nonlinear Schr\"odinger flow past two impenetrable obstacles. We numerically show that this collision is very similar to the dark soliton collisions in the one dimensional case. We observe that it is practically elastic and we measure the shifts of the solitons positions after their interaction