  We present a statistical description of the propagation of short pulses in
long optical fibers, taking into account the Kerr and nonlocal nonlinearities
on an equal footing. We use the Wigner approach on the modified nonlinear
Schroedinger equation to obtain a wave kinetic equation and a nonlinear
dispersion relation. The latter exhibit that the optical pulse decoherence
reduces the growth rate of the modulational instability, and thereby contribute
to the nonlinear stability of the pulses in long optical fibers. It is also
found that the interaction between spectral broadening and nonlocality tends to
extend the instability region.

Optics;Pattern Formation and Solitons