Effects of nonlocal dispersive interactions on self-trapping excitations

Abstract

A one-dimensional discrete nonlinear Schrödinger (NLS) model with the power dependence [formula presented] on the distance r of the dispersive interactions is proposed. The stationary states [formula presented] of the system are studied both analytically and numerically. Two types of stationary states are investigated: on-site and intersite states. It is shown that for s sufficiently large all features of the model are qualitatively the same as in the NLS model with a nearest-neighbor interaction. For s less than some critical value [formula presented], there is an interval of bistability where two stable stationary states exist at each excitation number N=[formula presented]|[formula presented][formula presented]. For cubic nonlinearity the bistability of on-site solitons may occur for dipole-dipole dispersive interaction (s=3), while [formula presented] for intersite solitons is close to 2.1. For increasing degree of nonlinearity σ, [formula presented] increases. The long-distance behavior of the intrinsically localized states depends on s. For s>3 their tails are exponential, while for 2