Effects of nonlocal dispersive interactions on self-trapping excitations

Yu.B. Gaididei, S.F. Mingaleev, Peter Leth Christiansen, Kim Rasmussen

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    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 > 3 their tails are exponential, while for 2 <s <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 <sigma + 1.
    Original languageEnglish
    JournalPhysical Review E. Statistical, Nonlinear, and Soft Matter Physics
    Volume55
    Issue number5
    Pages (from-to)6141-6149
    ISSN1063-651X
    DOIs
    Publication statusPublished - 1997

    Bibliographical note

    Copyright (1997) by the American Physical Society.

    Keywords

    • SYSTEMS
    • BREATHERS
    • INTRINSIC LOCALIZED MODES
    • POLYACETYLENE
    • STABILITY
    • RANGE INTERPARTICLE INTERACTIONS
    • 2-DIMENSIONAL ANHARMONIC LATTICES
    • SOLITON
    • DYNAMICS
    • NONLINEAR SCHRODINGER-EQUATION

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