Stable localized pulses and zigzag stripes in a two-dimensional diffractive-diffusive Ginzburg-Landau equation

Hidetsugu Sakaguchi, Boris A. Malomed

    Research output: Contribution to journalArticle

    14 Citations (Scopus)

    Abstract

    We introduce a model of a two-dimensional (2D) optical waveguide with Kerr nonlinearity, linear and quintic losses, cubic gain, and temporal-domain filtering. In the general case, temporal dispersion is also included, although it is not necessary. The model provides for description of a nonlinear planar waveguide incorporated into a closed optical cavity. It takes the form of a 2D cubic-quintic Ginzburg-Landau equation with an anisotropy of a novel type: the equation is diffractive in one direction, and diffusive in the other. By means of systematic simulations, we demonstrate that the model gives rise to stable fully localized 2D pulses, which are spatiotemporal "light bullets", existing due to the simultaneous balances between diffraction, dispersion, and Kerr nonlinearity, and between linear and quintic losses and cubic gain. A stability region of the 2D pulses is identified in the system's parameter space. Besides that, we also find that the model generates 1D patterns in the form of simple localized stripes, which may be stable, or may exhibit an instability transforming them into oblique stripes with zigzags. The straight and oblique stripes may stably coexist with the 2D pulse, but not with each other.

    Original languageEnglish
    Pages (from-to)91-100
    Number of pages10
    JournalPhysica D: Nonlinear Phenomena
    Volume159
    Issue number1-2
    DOIs
    Publication statusPublished - Nov 1 2001

    Fingerprint

    Landau-Ginzburg equations
    pulses
    nonlinearity
    optical waveguides
    waveguides
    anisotropy
    cavities
    diffraction
    simulation

    All Science Journal Classification (ASJC) codes

    • Statistical and Nonlinear Physics
    • Mathematical Physics
    • Condensed Matter Physics
    • Applied Mathematics

    Cite this

    Stable localized pulses and zigzag stripes in a two-dimensional diffractive-diffusive Ginzburg-Landau equation. / Sakaguchi, Hidetsugu; Malomed, Boris A.

    In: Physica D: Nonlinear Phenomena, Vol. 159, No. 1-2, 01.11.2001, p. 91-100.

    Research output: Contribution to journalArticle

    @article{4a2f82ddc1794c03a01d9cfb01382a06,
    title = "Stable localized pulses and zigzag stripes in a two-dimensional diffractive-diffusive Ginzburg-Landau equation",
    abstract = "We introduce a model of a two-dimensional (2D) optical waveguide with Kerr nonlinearity, linear and quintic losses, cubic gain, and temporal-domain filtering. In the general case, temporal dispersion is also included, although it is not necessary. The model provides for description of a nonlinear planar waveguide incorporated into a closed optical cavity. It takes the form of a 2D cubic-quintic Ginzburg-Landau equation with an anisotropy of a novel type: the equation is diffractive in one direction, and diffusive in the other. By means of systematic simulations, we demonstrate that the model gives rise to stable fully localized 2D pulses, which are spatiotemporal {"}light bullets{"}, existing due to the simultaneous balances between diffraction, dispersion, and Kerr nonlinearity, and between linear and quintic losses and cubic gain. A stability region of the 2D pulses is identified in the system's parameter space. Besides that, we also find that the model generates 1D patterns in the form of simple localized stripes, which may be stable, or may exhibit an instability transforming them into oblique stripes with zigzags. The straight and oblique stripes may stably coexist with the 2D pulse, but not with each other.",
    author = "Hidetsugu Sakaguchi and Malomed, {Boris A.}",
    year = "2001",
    month = "11",
    day = "1",
    doi = "10.1016/S0167-2789(01)00334-7",
    language = "English",
    volume = "159",
    pages = "91--100",
    journal = "Physica D: Nonlinear Phenomena",
    issn = "0167-2789",
    publisher = "Elsevier",
    number = "1-2",

    }

    TY - JOUR

    T1 - Stable localized pulses and zigzag stripes in a two-dimensional diffractive-diffusive Ginzburg-Landau equation

    AU - Sakaguchi, Hidetsugu

    AU - Malomed, Boris A.

    PY - 2001/11/1

    Y1 - 2001/11/1

    N2 - We introduce a model of a two-dimensional (2D) optical waveguide with Kerr nonlinearity, linear and quintic losses, cubic gain, and temporal-domain filtering. In the general case, temporal dispersion is also included, although it is not necessary. The model provides for description of a nonlinear planar waveguide incorporated into a closed optical cavity. It takes the form of a 2D cubic-quintic Ginzburg-Landau equation with an anisotropy of a novel type: the equation is diffractive in one direction, and diffusive in the other. By means of systematic simulations, we demonstrate that the model gives rise to stable fully localized 2D pulses, which are spatiotemporal "light bullets", existing due to the simultaneous balances between diffraction, dispersion, and Kerr nonlinearity, and between linear and quintic losses and cubic gain. A stability region of the 2D pulses is identified in the system's parameter space. Besides that, we also find that the model generates 1D patterns in the form of simple localized stripes, which may be stable, or may exhibit an instability transforming them into oblique stripes with zigzags. The straight and oblique stripes may stably coexist with the 2D pulse, but not with each other.

    AB - We introduce a model of a two-dimensional (2D) optical waveguide with Kerr nonlinearity, linear and quintic losses, cubic gain, and temporal-domain filtering. In the general case, temporal dispersion is also included, although it is not necessary. The model provides for description of a nonlinear planar waveguide incorporated into a closed optical cavity. It takes the form of a 2D cubic-quintic Ginzburg-Landau equation with an anisotropy of a novel type: the equation is diffractive in one direction, and diffusive in the other. By means of systematic simulations, we demonstrate that the model gives rise to stable fully localized 2D pulses, which are spatiotemporal "light bullets", existing due to the simultaneous balances between diffraction, dispersion, and Kerr nonlinearity, and between linear and quintic losses and cubic gain. A stability region of the 2D pulses is identified in the system's parameter space. Besides that, we also find that the model generates 1D patterns in the form of simple localized stripes, which may be stable, or may exhibit an instability transforming them into oblique stripes with zigzags. The straight and oblique stripes may stably coexist with the 2D pulse, but not with each other.

    UR - http://www.scopus.com/inward/record.url?scp=0035499882&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0035499882&partnerID=8YFLogxK

    U2 - 10.1016/S0167-2789(01)00334-7

    DO - 10.1016/S0167-2789(01)00334-7

    M3 - Article

    AN - SCOPUS:0035499882

    VL - 159

    SP - 91

    EP - 100

    JO - Physica D: Nonlinear Phenomena

    JF - Physica D: Nonlinear Phenomena

    SN - 0167-2789

    IS - 1-2

    ER -