  We study wave turbulence in systems with two special properties: a large
number of fields (large $N$) and a nonlinear interaction that is strongly local
in momentum space. The first property allows us to find the kinetic equation at
all interaction strengths -- both weak and strong, at leading order in $1/N$.
The second allows us to turn the kinetic equation -- an integral equation --
into a differential equation. We find stationary solutions for the occupation
number as a function of wave number, valid at all scales. As expected, on the
weak coupling end the solutions asymptote to Kolmogorov-Zakharov scaling. On
the strong coupling end, they asymptote to either the widely conjectured
generalized Phillips spectrum (also known as critical balance), or a
Kolmogorov-like scaling exponent.
