Radiating multimode dispersive shock waves.

We predict that dispersive shock waves can be observed in multimode fibers with a parabolic index profile despite competing with geometric parametric instability. Spatial self-imaging forces these shock waves to radiate at multiple resonant frequencies even in the absence of relevant higher-order dispersion. A simple phase-matching rule derived from a reduced model accurately describes such resonances in agreement with a full 1 + 3D model. This allows to interpret spectral reshaping of intense pulses occurring in the normal dispersion regime.