Abstract
A one-dimensional discrete nonlinear Schrödinger (NLS) model with the power dependence on the distance r of the dispersive interactions is proposed. The stationary states 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 , there is an interval of bistability where two stable stationary states exist at each excitation number N=|. For cubic nonlinearity the bistability of on-site solitons may occur for dipole-dipole dispersive interaction (s=3), while for intersite solitons is close to 2.1. For increasing degree of nonlinearity σ, increases. The long-distance behavior of the intrinsically localized states depends on s. For s>3 their tails are exponential, while for 2
DOI:https://doi.org/10.1103/PhysRevE.55.6141
©1997 American Physical Society