Localized excitations in discrete nonlinear Schrodinger systems: Effects of nonlocal dispersive interactions and noise

Kim Rasmussen, Peter Leth Christiansen, Magnus Johansson, Yuri B. Gaididei, S.F. Mingaleev

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    A one-dimensional discrete nonlinear Schrodinger (DNLS) model with the power dependence, r(-s) on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech-like are exploited and the results of both approaches are compared. Both on-site and inter-site stationary states sue investigated. It is shown that for s sufficiently large air features of the model me qualitatively the same as in the DNLS model with 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. The bistability of on-site solitons may occur for dipole-dipole dispersive interaction (s = 3), while s(cr) for inter-sire solitons is close to 2.1.

    In the framework of the DNLS equation with nearest-neighbor coupling we discuss the stability of highly localized, "breather-like", excitations under the influence of thermal fluctuations. Numerical analysis shows that the lifetime of the breather is aln,aps finite and in a large parameter region inversely proportional to the noise variance far fixed damping and nonlinearity. We also find that the decay rare of the breather decreases with increasing nonlinearity and with increasing damping. Copyright (C) 1998 Elsevier Science B.V.
    Original languageEnglish
    JournalPhysica D: Nonlinear Phenomena
    Volume113
    Issue number2-4
    Pages (from-to)134-151
    ISSN0167-2789
    DOIs
    Publication statusPublished - 1998

    Cite this

    Rasmussen, Kim ; Christiansen, Peter Leth ; Johansson, Magnus ; Gaididei, Yuri B. ; Mingaleev, S.F. / Localized excitations in discrete nonlinear Schrodinger systems: Effects of nonlocal dispersive interactions and noise. In: Physica D: Nonlinear Phenomena. 1998 ; Vol. 113, No. 2-4. pp. 134-151.
    @article{105c5b8d31fa4b719bc30161b0b48bdd,
    title = "Localized excitations in discrete nonlinear Schrodinger systems: Effects of nonlocal dispersive interactions and noise",
    abstract = "A one-dimensional discrete nonlinear Schrodinger (DNLS) model with the power dependence, r(-s) on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech-like are exploited and the results of both approaches are compared. Both on-site and inter-site stationary states sue investigated. It is shown that for s sufficiently large air features of the model me qualitatively the same as in the DNLS model with 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. The bistability of on-site solitons may occur for dipole-dipole dispersive interaction (s = 3), while s(cr) for inter-sire solitons is close to 2.1.In the framework of the DNLS equation with nearest-neighbor coupling we discuss the stability of highly localized, {"}breather-like{"}, excitations under the influence of thermal fluctuations. Numerical analysis shows that the lifetime of the breather is aln,aps finite and in a large parameter region inversely proportional to the noise variance far fixed damping and nonlinearity. We also find that the decay rare of the breather decreases with increasing nonlinearity and with increasing damping. Copyright (C) 1998 Elsevier Science B.V.",
    author = "Kim Rasmussen and Christiansen, {Peter Leth} and Magnus Johansson and Gaididei, {Yuri B.} and S.F. Mingaleev",
    year = "1998",
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    Localized excitations in discrete nonlinear Schrodinger systems: Effects of nonlocal dispersive interactions and noise. / Rasmussen, Kim; Christiansen, Peter Leth; Johansson, Magnus; Gaididei, Yuri B.; Mingaleev, S.F.

    In: Physica D: Nonlinear Phenomena, Vol. 113, No. 2-4, 1998, p. 134-151.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Localized excitations in discrete nonlinear Schrodinger systems: Effects of nonlocal dispersive interactions and noise

    AU - Rasmussen, Kim

    AU - Christiansen, Peter Leth

    AU - Johansson, Magnus

    AU - Gaididei, Yuri B.

    AU - Mingaleev, S.F.

    PY - 1998

    Y1 - 1998

    N2 - A one-dimensional discrete nonlinear Schrodinger (DNLS) model with the power dependence, r(-s) on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech-like are exploited and the results of both approaches are compared. Both on-site and inter-site stationary states sue investigated. It is shown that for s sufficiently large air features of the model me qualitatively the same as in the DNLS model with 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. The bistability of on-site solitons may occur for dipole-dipole dispersive interaction (s = 3), while s(cr) for inter-sire solitons is close to 2.1.In the framework of the DNLS equation with nearest-neighbor coupling we discuss the stability of highly localized, "breather-like", excitations under the influence of thermal fluctuations. Numerical analysis shows that the lifetime of the breather is aln,aps finite and in a large parameter region inversely proportional to the noise variance far fixed damping and nonlinearity. We also find that the decay rare of the breather decreases with increasing nonlinearity and with increasing damping. Copyright (C) 1998 Elsevier Science B.V.

    AB - A one-dimensional discrete nonlinear Schrodinger (DNLS) model with the power dependence, r(-s) on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech-like are exploited and the results of both approaches are compared. Both on-site and inter-site stationary states sue investigated. It is shown that for s sufficiently large air features of the model me qualitatively the same as in the DNLS model with 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. The bistability of on-site solitons may occur for dipole-dipole dispersive interaction (s = 3), while s(cr) for inter-sire solitons is close to 2.1.In the framework of the DNLS equation with nearest-neighbor coupling we discuss the stability of highly localized, "breather-like", excitations under the influence of thermal fluctuations. Numerical analysis shows that the lifetime of the breather is aln,aps finite and in a large parameter region inversely proportional to the noise variance far fixed damping and nonlinearity. We also find that the decay rare of the breather decreases with increasing nonlinearity and with increasing damping. Copyright (C) 1998 Elsevier Science B.V.

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    DO - 10.1016/S0167-2789(97)00261-3

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