Solitary excitations in discrete two-dimensional nonlinear Schrodinger models with dispersive dipole-dipole interactions

Peter Leth Christiansen, Yuri Borisovich Gaididei, M. Johansson, Kim Rasmussen, Vladimir Mezentsev, Jens Juul Rasmussen

    Research output: Contribution to journalJournal articleResearchpeer-review

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    Abstract

    The dynamics of discrete two-dimensional nonlinear Schrodinger models with long-range dispersive interactions is investigated. In particular, we focus on the cases where the dispersion arises from a dipole-dipole interaction, assuming the dipole moments at each lattice site to be aligned either in the lattice plane (anisotropic case) or perpendicular to the lattice plane (isotropic case). We investigate the nature of the linear dispersion relation for these two cases, and derive a criterion for the modulational instability of a plane wave with respect to long-wavelength perturbations. Furthermore, we study the on-site localized stationary states of the system numerically and analytically using a variational approach. In general, the narrow, intrinsically localized states are found to be stable, while broad, "continuumlike" excitations are unstable and may either collapse into intrinsically localized modes or disperse when a small perturbation is applied.
    Original languageEnglish
    JournalPhysical Review B Condensed Matter
    Volume57
    Issue number18
    Pages (from-to)11303-11318
    ISSN0163-1829
    DOIs
    Publication statusPublished - 1998

    Bibliographical note

    Copyright (1998) by the American Physical Society.

    Keywords

    • REGIMES
    • SYSTEMS
    • WAVE COLLAPSE
    • INTRINSIC LOCALIZED MODES
    • INSTABILITY
    • RANGE INTERPARTICLE INTERACTIONS
    • 2-DIMENSIONAL ANHARMONIC LATTICES
    • DYNAMICS
    • SOLITONS
    • EQUATIONS

    Cite this

    @article{3ef36ef5113a48b4a3cd7d650177352c,
    title = "Solitary excitations in discrete two-dimensional nonlinear Schrodinger models with dispersive dipole-dipole interactions",
    abstract = "The dynamics of discrete two-dimensional nonlinear Schrodinger models with long-range dispersive interactions is investigated. In particular, we focus on the cases where the dispersion arises from a dipole-dipole interaction, assuming the dipole moments at each lattice site to be aligned either in the lattice plane (anisotropic case) or perpendicular to the lattice plane (isotropic case). We investigate the nature of the linear dispersion relation for these two cases, and derive a criterion for the modulational instability of a plane wave with respect to long-wavelength perturbations. Furthermore, we study the on-site localized stationary states of the system numerically and analytically using a variational approach. In general, the narrow, intrinsically localized states are found to be stable, while broad, {"}continuumlike{"} excitations are unstable and may either collapse into intrinsically localized modes or disperse when a small perturbation is applied.",
    keywords = "REGIMES, SYSTEMS, WAVE COLLAPSE, INTRINSIC LOCALIZED MODES, INSTABILITY, RANGE INTERPARTICLE INTERACTIONS, 2-DIMENSIONAL ANHARMONIC LATTICES, DYNAMICS, SOLITONS, EQUATIONS",
    author = "Christiansen, {Peter Leth} and Gaididei, {Yuri Borisovich} and M. Johansson and Kim Rasmussen and Vladimir Mezentsev and {Juul Rasmussen}, Jens",
    note = "Copyright (1998) by the American Physical Society.",
    year = "1998",
    doi = "10.1103/PhysRevB.57.11303",
    language = "English",
    volume = "57",
    pages = "11303--11318",
    journal = "Physical Review B (Condensed Matter and Materials Physics)",
    issn = "1098-0121",
    publisher = "American Physical Society",
    number = "18",

    }

    Solitary excitations in discrete two-dimensional nonlinear Schrodinger models with dispersive dipole-dipole interactions. / Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.; Rasmussen, Kim; Mezentsev, Vladimir; Juul Rasmussen, Jens.

    In: Physical Review B Condensed Matter, Vol. 57, No. 18, 1998, p. 11303-11318.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Solitary excitations in discrete two-dimensional nonlinear Schrodinger models with dispersive dipole-dipole interactions

    AU - Christiansen, Peter Leth

    AU - Gaididei, Yuri Borisovich

    AU - Johansson, M.

    AU - Rasmussen, Kim

    AU - Mezentsev, Vladimir

    AU - Juul Rasmussen, Jens

    N1 - Copyright (1998) by the American Physical Society.

    PY - 1998

    Y1 - 1998

    N2 - The dynamics of discrete two-dimensional nonlinear Schrodinger models with long-range dispersive interactions is investigated. In particular, we focus on the cases where the dispersion arises from a dipole-dipole interaction, assuming the dipole moments at each lattice site to be aligned either in the lattice plane (anisotropic case) or perpendicular to the lattice plane (isotropic case). We investigate the nature of the linear dispersion relation for these two cases, and derive a criterion for the modulational instability of a plane wave with respect to long-wavelength perturbations. Furthermore, we study the on-site localized stationary states of the system numerically and analytically using a variational approach. In general, the narrow, intrinsically localized states are found to be stable, while broad, "continuumlike" excitations are unstable and may either collapse into intrinsically localized modes or disperse when a small perturbation is applied.

    AB - The dynamics of discrete two-dimensional nonlinear Schrodinger models with long-range dispersive interactions is investigated. In particular, we focus on the cases where the dispersion arises from a dipole-dipole interaction, assuming the dipole moments at each lattice site to be aligned either in the lattice plane (anisotropic case) or perpendicular to the lattice plane (isotropic case). We investigate the nature of the linear dispersion relation for these two cases, and derive a criterion for the modulational instability of a plane wave with respect to long-wavelength perturbations. Furthermore, we study the on-site localized stationary states of the system numerically and analytically using a variational approach. In general, the narrow, intrinsically localized states are found to be stable, while broad, "continuumlike" excitations are unstable and may either collapse into intrinsically localized modes or disperse when a small perturbation is applied.

    KW - REGIMES

    KW - SYSTEMS

    KW - WAVE COLLAPSE

    KW - INTRINSIC LOCALIZED MODES

    KW - INSTABILITY

    KW - RANGE INTERPARTICLE INTERACTIONS

    KW - 2-DIMENSIONAL ANHARMONIC LATTICES

    KW - DYNAMICS

    KW - SOLITONS

    KW - EQUATIONS

    U2 - 10.1103/PhysRevB.57.11303

    DO - 10.1103/PhysRevB.57.11303

    M3 - Journal article

    VL - 57

    SP - 11303

    EP - 11318

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

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

    SN - 1098-0121

    IS - 18

    ER -