Spatial dispersive shock waves generated in supersonic flow of Bose-Einstein condensate past slender body

Supersonic flow of Bose-Einstein condensate past macroscopic obstacles is studied theoretically. It is shown that in the case of large obstacles the Cherenkov cone transforms into a stationary spatial shock wave which consists of a number of spatial dark solitons. Analytical theory is developed for the case of obstacles having a form of a slender body. This theory explains qualitatively the properties of such shocks observed in recent experiments on nonlinear dynamics of condensates of dilute alkali gases.