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In dispersive media, hydrodynamic singularities are resolved by coherentwavetrains known as dispersive shock waves (DSWs). Only dynamically expanding,temporal DSWs are possible in one-dimensional media. The additional degree offreedom inherent in two-dimensional media allows for the generation oftime-independent DSWs that exhibit spatial expansion. Spatial oblique DSWs,dispersive analogs of oblique shocks in classical media, are constructedutilizing Whitham modulation theory for a class of nonlinear Schr\"{o}dingerboundary value problems. Self-similar, simple wave solutions of the modulationequations yield relations between the DSW's orientation and theupstream/downstream flow fields. Time dependent numerical simulationsdemonstrate a convective or absolute instability of oblique DSWs in supersonicflow over obstacles. The convective instability results in an effectivestabilization of the DSW.

Oblique spatial dispersive shock waves in nonlinear Schr\"odinger flows