Solitary excitations in discrete two-dimensional nonlinear Schrödinger models with dispersive dipole-dipole interactions

The dynamics of discrete two-dimensional nonlinear Schrödinger models with long-range dispersive interactions is investigated. In particular, we focus on the cases where the dispersion arises from a dipole-dipole interaction, assuming the dipole moments at each lattice site to be aligned either in the lattice plane (anisotropic case) or perpendicular to the lattice plane (isotropic case). We investigate the nature of the linear dispersion relation for these two cases, and derive a criterion for the modulational instability of a plane wave with respect to long-wavelength perturbations. Furthermore, we study the on-site localized stationary states of the system numerically and analytically using a variational approach. In general, the narrow, intrinsically localized states are found to be stable, while broad, “continuumlike” excitations are unstable and may either collapse into intrinsically localized modes or disperse when a small perturbation is applied.