  We consider the step Riemann problem for the system of equations describing
the propagation of a coherent light beam in nematic liquid crystals, which is a
general system describing nonlinear wave propagation in a number of different
physical applications. While the equation governing the light beam is of
defocusing nonlinear Schr\"odinger equation type, the dispersive shock wave
(DSW) generated from this initial condition has major differences from the
standard DSW solution of the defocusing nonlinear Schr\"odinger equation. In
particular, it is found that the DSW has positive polarity and generates
resonant radiation which propagates ahead of it. Remarkably, the velocity of
the lead soliton of the DSW is determined by the classical shock velocity. The
solution for the radiative wavetrain is obtained using the WKB approximation.
It is shown that for sufficiently small initial jumps the nematic DSW is
asymptotically governed by a Korteweg-de Vries equation with fifth order
dispersion, which explicitly shows the resonance generating the radiation ahead
of the DSW. The constructed asymptotic theory is shown to be in good agreement
with the results of direct numerical simulations.
