Modulation Instability of Two-Dimensional Dipolar Bose-Einstein Condensate in a Deep Optical Lattice

We study the stability of the continuous waves in the pancake shaped dipolar Bose-Einstein condensate trapped in the strong optical lattice potential with the coexisting local (the short-range s-wave) interaction and nonlocal (the dipole-dipole) interactions between the condensate atoms. The system is modeled by two two-dimensional discrete models derived from the Gross-Pitaevskii equation accounting the dipole-dipole interactions: discrete nonlinear Schrödinger equation with cubic nonlinearity and nonpolynomial Schrödinger equation. The corresponding dispersion relations are calculated analytically and the regions of the modulation instability in the parametric space are summarized into the stability diagrams.