Resonant radiation shed by dispersive shock waves

We analyze resonant radiation emitted by dispersive shock waves owing to higher-order dispersive corrections of the leading term in the defocusing nonlinear Schrödinger equation. We give criteria for calculating the radiated frequency based on an analytical estimate of the shock velocity and reveal a diversity of scenarios controllable via the corrections, ranging from the radiation-induced transition of the dispersive shock into a classical-type shock to the qualitative modification of the underlying gradient catastrophe or the competition between different breaking mechanisms.