Stabilization of nonlinear excitations by disorder

Peter Leth Christiansen, Yuri Borisovich Gaididei, M. Johansson, Kim Rasmussen, D. Usero, L Vazquez

    Research output: Contribution to journalJournal articleResearchpeer-review

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    Abstract

    Using analytical and numerical techniques we analyze the static and dynamical properties of solitonlike excitations in the presence of parametric disorder in the one-dimensional nonlinear Schrodinger equation with a homogeneous power nonlinearity. Both the continuum and the discrete problem are investigated. We find that otherwise unstable excitations can be stabilized by the presence of disorder in the continuum problem. For the very narrow excitations of the discrete problem we find that the disorder has no effect on the averaged behavior. Finally, we show that the disorder can be applied to induce a high degree of controllability of the spatial extent of the stable excitations in the continuum system.
    Original languageEnglish
    JournalPhysical Review B
    Volume56
    Issue number22
    Pages (from-to)14407-14413
    ISSN2469-9950
    DOIs
    Publication statusPublished - 1998

    Bibliographical note

    Copyright (1997) by the American Physical Society.

    Keywords

    • LOCALIZATION
    • SCHRODINGER-EQUATION
    • PROPAGATION
    • STABILITY
    • DYNAMICS
    • BLOW-UP
    • 2-DIMENSIONAL SOLITONS
    • DISCRETE-SYSTEMS
    • SCHROEDINGER EQUATIONS
    • COMPETITION

    Cite this

    Christiansen, Peter Leth ; Gaididei, Yuri Borisovich ; Johansson, M. ; Rasmussen, Kim ; Usero, D. ; Vazquez, L. / Stabilization of nonlinear excitations by disorder. In: Physical Review B. 1998 ; Vol. 56, No. 22. pp. 14407-14413.
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    title = "Stabilization of nonlinear excitations by disorder",
    abstract = "Using analytical and numerical techniques we analyze the static and dynamical properties of solitonlike excitations in the presence of parametric disorder in the one-dimensional nonlinear Schrodinger equation with a homogeneous power nonlinearity. Both the continuum and the discrete problem are investigated. We find that otherwise unstable excitations can be stabilized by the presence of disorder in the continuum problem. For the very narrow excitations of the discrete problem we find that the disorder has no effect on the averaged behavior. Finally, we show that the disorder can be applied to induce a high degree of controllability of the spatial extent of the stable excitations in the continuum system.",
    keywords = "LOCALIZATION, SCHRODINGER-EQUATION, PROPAGATION, STABILITY, DYNAMICS, BLOW-UP, 2-DIMENSIONAL SOLITONS, DISCRETE-SYSTEMS, SCHROEDINGER EQUATIONS, COMPETITION",
    author = "Christiansen, {Peter Leth} and Gaididei, {Yuri Borisovich} and M. Johansson and Kim Rasmussen and D. Usero and L Vazquez",
    note = "Copyright (1997) by the American Physical Society.",
    year = "1998",
    doi = "10.1103/PhysRevB.56.14407",
    language = "English",
    volume = "56",
    pages = "14407--14413",
    journal = "Physical Review B (Condensed Matter and Materials Physics)",
    issn = "1098-0121",
    publisher = "American Physical Society",
    number = "22",

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    Christiansen, PL, Gaididei, YB, Johansson, M, Rasmussen, K, Usero, D & Vazquez, L 1998, 'Stabilization of nonlinear excitations by disorder', Physical Review B, vol. 56, no. 22, pp. 14407-14413. https://doi.org/10.1103/PhysRevB.56.14407

    Stabilization of nonlinear excitations by disorder. / Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.; Rasmussen, Kim; Usero, D.; Vazquez, L.

    In: Physical Review B, Vol. 56, No. 22, 1998, p. 14407-14413.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Stabilization of nonlinear excitations by disorder

    AU - Christiansen, Peter Leth

    AU - Gaididei, Yuri Borisovich

    AU - Johansson, M.

    AU - Rasmussen, Kim

    AU - Usero, D.

    AU - Vazquez, L

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

    PY - 1998

    Y1 - 1998

    N2 - Using analytical and numerical techniques we analyze the static and dynamical properties of solitonlike excitations in the presence of parametric disorder in the one-dimensional nonlinear Schrodinger equation with a homogeneous power nonlinearity. Both the continuum and the discrete problem are investigated. We find that otherwise unstable excitations can be stabilized by the presence of disorder in the continuum problem. For the very narrow excitations of the discrete problem we find that the disorder has no effect on the averaged behavior. Finally, we show that the disorder can be applied to induce a high degree of controllability of the spatial extent of the stable excitations in the continuum system.

    AB - Using analytical and numerical techniques we analyze the static and dynamical properties of solitonlike excitations in the presence of parametric disorder in the one-dimensional nonlinear Schrodinger equation with a homogeneous power nonlinearity. Both the continuum and the discrete problem are investigated. We find that otherwise unstable excitations can be stabilized by the presence of disorder in the continuum problem. For the very narrow excitations of the discrete problem we find that the disorder has no effect on the averaged behavior. Finally, we show that the disorder can be applied to induce a high degree of controllability of the spatial extent of the stable excitations in the continuum system.

    KW - LOCALIZATION

    KW - SCHRODINGER-EQUATION

    KW - PROPAGATION

    KW - STABILITY

    KW - DYNAMICS

    KW - BLOW-UP

    KW - 2-DIMENSIONAL SOLITONS

    KW - DISCRETE-SYSTEMS

    KW - SCHROEDINGER EQUATIONS

    KW - COMPETITION

    U2 - 10.1103/PhysRevB.56.14407

    DO - 10.1103/PhysRevB.56.14407

    M3 - Journal article

    VL - 56

    SP - 14407

    EP - 14413

    JO - Physical Review B (Condensed Matter and Materials Physics)

    JF - Physical Review B (Condensed Matter and Materials Physics)

    SN - 1098-0121

    IS - 22

    ER -