Modulation Instability in Two-dimensional Nonlinear Schrodinger Lattice Models with Dispersion and Long-range Interactions

"The problem of modulation instability of continuous wave and array soliton solutions in the framework of a two-dimensional continuum-discrete nonlinear Schrodinger lattice model which accounts for dispersion and ling-range interactIONS BETWEEN ELEMENTS, IS INVESTIGATED. APPLICATION OF THE LINEAR STABILITY ANALYSIS BASED ON AN ENERGETIC PRINCIPLE AND A VARIATIONAL APPROACH, WHICH WERE ORIGINALLY DEVELOPED FOR THE CONTINUUM NONLINEAR SCHRODINGER MODEL, IS PROPOSED. Analytical expressions for the corresponding instability thresholds and the growth rate spectra are calculated.