  In dispersive media, hydrodynamic singularities are resolved by coherent
wavetrains known as dispersive shock waves (DSWs). Only dynamically expanding,
temporal DSWs are possible in one-dimensional media. The additional degree of
freedom inherent in two-dimensional media allows for the generation of
time-independent DSWs that exhibit spatial expansion. Spatial oblique DSWs,
dispersive analogs of oblique shocks in classical media, are constructed
utilizing Whitham modulation theory for a class of nonlinear Schr\"{o}dinger
boundary value problems. Self-similar, simple wave solutions of the modulation
equations yield relations between the DSW's orientation and the
upstream/downstream flow fields. Time dependent numerical simulations
demonstrate a convective or absolute instability of oblique DSWs in supersonic
flow over obstacles. The convective instability results in an effective
stabilization of the DSW.
