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.PACS numbers: 05.45. Yv, 63.20.Ry, 63.20.Pw Nonlinear wave propagation models are of importance in a wide variety of settings, such as in nonlinear optics [1,2], in water wave propagation [3], and in plasma systems [4]. Moreover, also discrete systems show important nonlinear properties that give rise to solitary structures in e.g. lattices (see, e.g. [5] and references therein for a review). The discrete Salerno model [6] combines onsite and intersite nonlinear terms in a lattice in order to encompass the different characteristics of nonlinear integrable and non-integrable lattice models. It has also been discovered as an asymptotic form of the Gross-Pitaevskii equation, with applications to Bose-Einstein condensation of atoms with magnetic moments in deep optical lattice traps [7,8]. Recently, the continuum limit of the Salerno model with focusing onsite and defocusing intersite nonlinearities was investigated [8] and soliton solutions were found.In this Brief Report, we will investigate the modulational instability properties of the general continuum limit of the Salerno model. Furthermore, the effects of random phased wave packets on the stability properties will be studied using the Wigner formalism. Results regarding the effect of random pulse phases will be given.The Salerno model was derived as a quantum modified discrete nonlinear Schrödinger equation, giving the time evolution of the field amplitude on the lattice. The relevant equation takes the form [6]where Φ n = Φ(t, x n ) is the field amplitude on the nth lattice site located at x n and ν and µ are the real parameters determining the strength of the onsite and intersite * Also