  The statistical properties of the Salerno model is investigated.
  In particular, a comparison between the coherent and partially coherent wave
modes is made for the case of a random phased wave packet. It is found that the
random phased induced spectral broadening gives rise to damping of
instabilities, but also a broadening of the instability region in
quasi-particle momentum space. The results can be of significance for
condensation of magnetic moment bosons in deep optical lattices.
