  The statistical evolution of ensembles of random, weakly-interacting waves is
governed by wave kinetic equations. To simplify the analysis, one frequently
works with reduced differential models of the wave kinetics. However, the
conditions for deriving such reduced models are seldom justified
self-consistently. Here, we derive a reduced model for the wave kinetics of the
Schr{\"o}dinger-Helmholtz equations in two spatial dimensions, which constitute
a model for the dynamics of light in a spatially-nonlocal, nonlinear optical
medium. This model has the property of sharply localising the frequencies of
the interacting waves into two pairs, allowing for a rigorous and
self-consistent derivation of what we term the semilocal approximation model
(SLAM) of the wave kinetic equation. Using the SLAM, we study the stationary
spectra of Schr{\"o}dinger-Helmholtz wave turbulence, and characterise the
spectra that carry energy downscale, and waveaction upscale, in a
forced-dissipated setup. The latter involves a nonlocal transfer of waveaction,
in which waves at the forcing scale mediate the interactions of waves at every
larger scale. This is in contrast to the energy cascade, which involves local
scale-by-scale interactions, familiar from other wave turbulent systems and
from classical hydrodynamical turbulence.
