Modulation instability in two-dimensional nonlinear Schrodinger lattice models with dispersion and long-range interactions

Abstract

The problem of modulation instability of continuous wave and array soliton solutions within the framework of a two-dimensional continuum-discrete nonlinear Schrodinger lattice model, which accounts for dispersion and long-range interactions between elements, is investigated. The linear stability analysis based on an energy principle and a variational approach, which were originally developed for the continuum nonlinear Schrodinger model, is proposed. Regions of instability are identified and analytical expressions for the corresponding thresholds and the growth rate spectra are calculated.