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 = Sigma(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 \textgreater 3 their tails are exponential, while for 2 \textless s \textless 3 they are algebraic. In the continuum limit the model is described by a nonlocal MLS equation for which the stability criterion for the ground state is shown to be s \textless sigma + 1.

Keywords: nonlinear schrodinger-equation; intrinsic localized modes; 2- dimensional anharmonic lattices; range interparticle interactions; dynamics; soliton; polyacetylene; breathers; stability; systems

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