  We study analytically and numerically a kind of diffractive resonant
radiation emitted by spatial solitons, which is generated in waveguide arrays
with Kerr nonlinearity. The phase matching condition between soliton and
radiation is derived and agrees well with direct pulse propagation simulations.
The folded dispersion due to the Brillouin zone leads to a peculiar anomalous
soliton recoil that we describe in detail. A linear potential applied across
the array generates the analogue of the Raman self-frequency shift in optical
fibers, only now applied to the wavenumber. We demonstrate that it is possible
to mimic closely temporal fiber-optical dynamics, unveiling the new effects of
wavenumber-supercontinuum generation and the compensation of the 'soliton
self-wavenumber shift' by the emitted diffractive radiation. This work paves
the way for designing unique optical devices that generate spectrally broad
supercontinua with a controllable directionality.
