Abstract
The influence of long-range interactions on the stability of stationary solutions of triangular lattices described by the continuum-discrete nonlinear Schrodinger equation is analyzed. By virtue of the linear stability analysis and a variational approach we demonstrate that both soliton array and continuous-wave solutions are modulationally unstable. Analytical expressions for instability thresholds and growth rate spectra are presented and compared with the corresponding results in the approximation of a nearest neighbor interaction.
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