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., ). Yet another type of nonlinear wave patterns has been observed in
a series of experiments on the BEC flow past macroscopic obstacles . In  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 . Here we shall present the theory of these new structures in BEC.