Statistical description of short pulses in long optical fibers: Effects   of nonlocality
  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. 
P.K. Shukla and M. Marklund