Dynamics of breathers in discrete nonlinear Schrodinger models

Peter Leth Christiansen, Magnus Johansson, Serge Aubry, Yuri B. Gaididei, Kim Rasmussen

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized vortex-like solutions. We also show that stationary on-site localized excitations can have internal 'breathing' modes which are spatially localized and symmetric. The excitation of these modes leads to slowly decaying, quasiperiodic oscillations. Finally, we show that for some generalizations of the DNLS equation where bistability occurs, a controlled switching between stable states is possible by exciting an internal breathing mode above a threshold value. (C) 1998 Elsevier Science B.V.
    Original languageEnglish
    JournalPhysica D: Nonlinear Phenomena
    Volume119
    Issue number1-2
    Pages (from-to)115-124
    ISSN0167-2789
    DOIs
    Publication statusPublished - 1998

    Cite this

    Christiansen, Peter Leth ; Johansson, Magnus ; Aubry, Serge ; Gaididei, Yuri B. ; Rasmussen, Kim. / Dynamics of breathers in discrete nonlinear Schrodinger models. In: Physica D: Nonlinear Phenomena. 1998 ; Vol. 119, No. 1-2. pp. 115-124.
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    title = "Dynamics of breathers in discrete nonlinear Schrodinger models",
    abstract = "We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized vortex-like solutions. We also show that stationary on-site localized excitations can have internal 'breathing' modes which are spatially localized and symmetric. The excitation of these modes leads to slowly decaying, quasiperiodic oscillations. Finally, we show that for some generalizations of the DNLS equation where bistability occurs, a controlled switching between stable states is possible by exciting an internal breathing mode above a threshold value. (C) 1998 Elsevier Science B.V.",
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    Dynamics of breathers in discrete nonlinear Schrodinger models. / Christiansen, Peter Leth; Johansson, Magnus; Aubry, Serge; Gaididei, Yuri B.; Rasmussen, Kim.

    In: Physica D: Nonlinear Phenomena, Vol. 119, No. 1-2, 1998, p. 115-124.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Dynamics of breathers in discrete nonlinear Schrodinger models

    AU - Christiansen, Peter Leth

    AU - Johansson, Magnus

    AU - Aubry, Serge

    AU - Gaididei, Yuri B.

    AU - Rasmussen, Kim

    PY - 1998

    Y1 - 1998

    N2 - We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized vortex-like solutions. We also show that stationary on-site localized excitations can have internal 'breathing' modes which are spatially localized and symmetric. The excitation of these modes leads to slowly decaying, quasiperiodic oscillations. Finally, we show that for some generalizations of the DNLS equation where bistability occurs, a controlled switching between stable states is possible by exciting an internal breathing mode above a threshold value. (C) 1998 Elsevier Science B.V.

    AB - We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized vortex-like solutions. We also show that stationary on-site localized excitations can have internal 'breathing' modes which are spatially localized and symmetric. The excitation of these modes leads to slowly decaying, quasiperiodic oscillations. Finally, we show that for some generalizations of the DNLS equation where bistability occurs, a controlled switching between stable states is possible by exciting an internal breathing mode above a threshold value. (C) 1998 Elsevier Science B.V.

    U2 - 10.1016/S0167-2789(98)00070-0

    DO - 10.1016/S0167-2789(98)00070-0

    M3 - Journal article

    VL - 119

    SP - 115

    EP - 124

    JO - Physica D: Nonlinear Phenomena

    JF - Physica D: Nonlinear Phenomena

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