NONLINEAR SCHRODINGER FLOW PAST AN OBSTACLE IN ONE-DIMENSION

The flow of a one-dimensional defocusing nonlinear Schrodinger fluid p ast an obstacle is investigated. Below an obstacle-dependent critical velocity, a steady dissipationless motion is possible and the how prof ile is determined analytically in several cases. At the critical veloc ity, the steady flow solution disappears by merging with an unstable s olution in a usual saddle-node bifurcation. It is argued that this uns table solution represents the transition state for emission of gray so litons. The barrier for soliton emission is explicitly computed and va nishes at the critical velocity. Above the critical velocity, the flow becomes unsteady and its characteristics are studied numerically. It is found that gray solitons are repeatedly emitted by the obstacle and propagate downstream. Upstream propagating dispersive waves are emitt ed concurrently. A hydraulic approximation is used to interpret these results.