Abstract: A one-dimensional discrete nonlinear Schrodinger (NLS) model with the power dependence r^{-s} on the distance r of the dispersive interactions is proposed. The stationary states \psi_n 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 s_{cr}, there is an interval of bistability where two stable stationary states exist at each excitation number N = \sum_n |\psi_n|^2. For cubic nonlinearity the bistability of on-site solitons may occur for dipole-dipole dispersive interaction (s = 3), while s_{cr} for intersite solitons is close to 2.1. For increasing degree of nonlinearity sigma, s_{cr} increases. The long-distance behavior of the intrinsically localized states depends on s. For s>3 their tails are exponential, while for 2

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