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

    Cite this

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    title = "Effects of nonlocal dispersive interactions on self-trapping excitations",
    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.",
    keywords = "SYSTEMS, BREATHERS, INTRINSIC LOCALIZED MODES, POLYACETYLENE, STABILITY, RANGE INTERPARTICLE INTERACTIONS, 2-DIMENSIONAL ANHARMONIC LATTICES, SOLITON, DYNAMICS, NONLINEAR SCHRODINGER-EQUATION",
    author = "Yu.B. Gaididei and S.F. Mingaleev and Christiansen, {Peter Leth} and Kim Rasmussen",
    note = "Copyright (1997) by the American Physical Society.",
    year = "1997",
    doi = "10.1103/PhysRevE.55.6141",
    language = "English",
    volume = "55",
    pages = "6141--6149",
    journal = "Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)",
    issn = "2470-0045",
    publisher = "American Physical Society",
    number = "5",

    }

    Effects of nonlocal dispersive interactions on self-trapping excitations. / Gaididei, Yu.B.; Mingaleev, S.F.; Christiansen, Peter Leth; Rasmussen, Kim.

    In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, Vol. 55, No. 5, 1997, p. 6141-6149.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Effects of nonlocal dispersive interactions on self-trapping excitations

    AU - Gaididei, Yu.B.

    AU - Mingaleev, S.F.

    AU - Christiansen, Peter Leth

    AU - Rasmussen, Kim

    N1 - Copyright (1997) by the American Physical Society.

    PY - 1997

    Y1 - 1997

    N2 - 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.

    AB - 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.

    KW - SYSTEMS

    KW - BREATHERS

    KW - INTRINSIC LOCALIZED MODES

    KW - POLYACETYLENE

    KW - STABILITY

    KW - RANGE INTERPARTICLE INTERACTIONS

    KW - 2-DIMENSIONAL ANHARMONIC LATTICES

    KW - SOLITON

    KW - DYNAMICS

    KW - NONLINEAR SCHRODINGER-EQUATION

    U2 - 10.1103/PhysRevE.55.6141

    DO - 10.1103/PhysRevE.55.6141

    M3 - Journal article

    VL - 55

    SP - 6141

    EP - 6149

    JO - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

    JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

    SN - 2470-0045

    IS - 5

    ER -