Motional Dressed States in a Bose-Einstein Condensate: Superfluidity at Supersonic Speed

We present an exact analytic solution of a nonlinear Schrodinger field interacting with a moving potential (obstacle) at supersonic speed. We discover conditions under which the field can form a stable shape-invariant structure localized around the obstacle-a dressing effect that protects the field against excitations by the obstacle. Such an effect demonstrates the existence of frictionless motion beyond the conventionally defined critical velocity.