Instabilities and splitting of pulses in coupled Ginzburg-Landau equations

Hidetsugu Sakaguchi, Boris A. Malomed

    Research output: Contribution to journalArticle

    18 Citations (Scopus)

    Abstract

    We introduce a general system of two coupled cubic complex Ginzburg-Landau (GL) equations that admits exact solitary-pulse (SP) solutions with a stable zero background. Besides representing a class of systems of the GL type, it also describes a dual-core nonlinear optical fiber with gain in one core and losses in the other. By means of systematic simulations, we study generic transformations of SPs in this system, which turn out to be: cascading multiplication of pulses through a subcritical Hopf bifurcation, which eventually leads to a spatio-temporal chaos; splitting of SP into stable traveling pulses; and a symmetry-breaking bifurcation transforming a standing SP into a traveling one. In some parameter region, the Hopf bifurcation is found to be supercritical, which gives rise to stable breathers. Travelling breathers are also possible in the system considered. In a certain parameter region, stable standing SPs, moving permanent-shape ones, and traveling breathers all coexist. In that case, we study collisions between various types of the pulses, which, generally, prove to be strongly inelastic.

    Original languageEnglish
    Pages (from-to)229-239
    Number of pages11
    JournalPhysica D: Nonlinear Phenomena
    Volume154
    Issue number3-4
    DOIs
    Publication statusPublished - Jun 15 2001

    Fingerprint

    Landau-Ginzburg equations
    pulses
    multiplication
    chaos
    broken symmetry
    optical fibers
    collisions
    simulation

    All Science Journal Classification (ASJC) codes

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

    Cite this

    Instabilities and splitting of pulses in coupled Ginzburg-Landau equations. / Sakaguchi, Hidetsugu; Malomed, Boris A.

    In: Physica D: Nonlinear Phenomena, Vol. 154, No. 3-4, 15.06.2001, p. 229-239.

    Research output: Contribution to journalArticle

    @article{bcb6db726d3b4ee792bfdb26ae03512f,
    title = "Instabilities and splitting of pulses in coupled Ginzburg-Landau equations",
    abstract = "We introduce a general system of two coupled cubic complex Ginzburg-Landau (GL) equations that admits exact solitary-pulse (SP) solutions with a stable zero background. Besides representing a class of systems of the GL type, it also describes a dual-core nonlinear optical fiber with gain in one core and losses in the other. By means of systematic simulations, we study generic transformations of SPs in this system, which turn out to be: cascading multiplication of pulses through a subcritical Hopf bifurcation, which eventually leads to a spatio-temporal chaos; splitting of SP into stable traveling pulses; and a symmetry-breaking bifurcation transforming a standing SP into a traveling one. In some parameter region, the Hopf bifurcation is found to be supercritical, which gives rise to stable breathers. Travelling breathers are also possible in the system considered. In a certain parameter region, stable standing SPs, moving permanent-shape ones, and traveling breathers all coexist. In that case, we study collisions between various types of the pulses, which, generally, prove to be strongly inelastic.",
    author = "Hidetsugu Sakaguchi and Malomed, {Boris A.}",
    year = "2001",
    month = "6",
    day = "15",
    doi = "10.1016/S0167-2789(01)00243-3",
    language = "English",
    volume = "154",
    pages = "229--239",
    journal = "Physica D: Nonlinear Phenomena",
    issn = "0167-2789",
    publisher = "Elsevier",
    number = "3-4",

    }

    TY - JOUR

    T1 - Instabilities and splitting of pulses in coupled Ginzburg-Landau equations

    AU - Sakaguchi, Hidetsugu

    AU - Malomed, Boris A.

    PY - 2001/6/15

    Y1 - 2001/6/15

    N2 - We introduce a general system of two coupled cubic complex Ginzburg-Landau (GL) equations that admits exact solitary-pulse (SP) solutions with a stable zero background. Besides representing a class of systems of the GL type, it also describes a dual-core nonlinear optical fiber with gain in one core and losses in the other. By means of systematic simulations, we study generic transformations of SPs in this system, which turn out to be: cascading multiplication of pulses through a subcritical Hopf bifurcation, which eventually leads to a spatio-temporal chaos; splitting of SP into stable traveling pulses; and a symmetry-breaking bifurcation transforming a standing SP into a traveling one. In some parameter region, the Hopf bifurcation is found to be supercritical, which gives rise to stable breathers. Travelling breathers are also possible in the system considered. In a certain parameter region, stable standing SPs, moving permanent-shape ones, and traveling breathers all coexist. In that case, we study collisions between various types of the pulses, which, generally, prove to be strongly inelastic.

    AB - We introduce a general system of two coupled cubic complex Ginzburg-Landau (GL) equations that admits exact solitary-pulse (SP) solutions with a stable zero background. Besides representing a class of systems of the GL type, it also describes a dual-core nonlinear optical fiber with gain in one core and losses in the other. By means of systematic simulations, we study generic transformations of SPs in this system, which turn out to be: cascading multiplication of pulses through a subcritical Hopf bifurcation, which eventually leads to a spatio-temporal chaos; splitting of SP into stable traveling pulses; and a symmetry-breaking bifurcation transforming a standing SP into a traveling one. In some parameter region, the Hopf bifurcation is found to be supercritical, which gives rise to stable breathers. Travelling breathers are also possible in the system considered. In a certain parameter region, stable standing SPs, moving permanent-shape ones, and traveling breathers all coexist. In that case, we study collisions between various types of the pulses, which, generally, prove to be strongly inelastic.

    UR - http://www.scopus.com/inward/record.url?scp=0035877071&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0035877071&partnerID=8YFLogxK

    U2 - 10.1016/S0167-2789(01)00243-3

    DO - 10.1016/S0167-2789(01)00243-3

    M3 - Article

    VL - 154

    SP - 229

    EP - 239

    JO - Physica D: Nonlinear Phenomena

    JF - Physica D: Nonlinear Phenomena

    SN - 0167-2789

    IS - 3-4

    ER -