Travelling waves in a singularly perturbed sine-Gordon equations

G.L.A. Derks, Gianne Derks, Arjen Doelman, Stephanus A. van Gils, T.P.P. Visser

    Research output: Contribution to journalArticleAcademicpeer-review

    15 Citations (Scopus)

    Abstract

    We determine the linearised stability of travelling front solutions of a perturbed sine-Gordon equation. This equation models the long Josephson junction using the RCSJ model for currents across the junction and includes surface resistance for currents along the junction. The travelling waves correspond to the so-called fluxons and their linear stability is determined by calculating the Evans function. Surface resistance corresponds to a singular perturbation term in the governing equation, which specifically complicates the computation of the corresponding Evans function. Both the flow of quasi-particles across and along the junction stabilise the waves.
    Original languageEnglish
    Pages (from-to)40-70
    JournalPhysica D
    Volume180
    Issue number1-2
    DOIs
    Publication statusPublished - 2003

    Fingerprint

    sine-Gordon equation
    Evans Function
    Surface resistance
    Sine-Gordon Equation
    Singularly Perturbed
    traveling waves
    Traveling Wave
    Travelling Fronts
    Josephson Junction
    Quasiparticles
    Linear Stability
    Singular Perturbation
    Governing equation
    elementary excitations
    Josephson junctions
    Term
    Model
    perturbation
    Resistance

    Keywords

    • METIS-211866
    • Evans function
    • IR-74894
    • Perturbed sine-Gordon equation
    • Travelling waves

    Cite this

    Derks, G.L.A. ; Derks, Gianne ; Doelman, Arjen ; van Gils, Stephanus A. ; Visser, T.P.P. / Travelling waves in a singularly perturbed sine-Gordon equations. In: Physica D. 2003 ; Vol. 180, No. 1-2. pp. 40-70.
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    abstract = "We determine the linearised stability of travelling front solutions of a perturbed sine-Gordon equation. This equation models the long Josephson junction using the RCSJ model for currents across the junction and includes surface resistance for currents along the junction. The travelling waves correspond to the so-called fluxons and their linear stability is determined by calculating the Evans function. Surface resistance corresponds to a singular perturbation term in the governing equation, which specifically complicates the computation of the corresponding Evans function. Both the flow of quasi-particles across and along the junction stabilise the waves.",
    keywords = "METIS-211866, Evans function, IR-74894, Perturbed sine-Gordon equation, Travelling waves",
    author = "G.L.A. Derks and Gianne Derks and Arjen Doelman and {van Gils}, {Stephanus A.} and T.P.P. Visser",
    year = "2003",
    doi = "10.1016/S0167-2789(03)00050-2",
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    Derks, GLA, Derks, G, Doelman, A, van Gils, SA & Visser, TPP 2003, 'Travelling waves in a singularly perturbed sine-Gordon equations', Physica D, vol. 180, no. 1-2, pp. 40-70. https://doi.org/10.1016/S0167-2789(03)00050-2

    Travelling waves in a singularly perturbed sine-Gordon equations. / Derks, G.L.A.; Derks, Gianne; Doelman, Arjen; van Gils, Stephanus A.; Visser, T.P.P.

    In: Physica D, Vol. 180, No. 1-2, 2003, p. 40-70.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Travelling waves in a singularly perturbed sine-Gordon equations

    AU - Derks, G.L.A.

    AU - Derks, Gianne

    AU - Doelman, Arjen

    AU - van Gils, Stephanus A.

    AU - Visser, T.P.P.

    PY - 2003

    Y1 - 2003

    N2 - We determine the linearised stability of travelling front solutions of a perturbed sine-Gordon equation. This equation models the long Josephson junction using the RCSJ model for currents across the junction and includes surface resistance for currents along the junction. The travelling waves correspond to the so-called fluxons and their linear stability is determined by calculating the Evans function. Surface resistance corresponds to a singular perturbation term in the governing equation, which specifically complicates the computation of the corresponding Evans function. Both the flow of quasi-particles across and along the junction stabilise the waves.

    AB - We determine the linearised stability of travelling front solutions of a perturbed sine-Gordon equation. This equation models the long Josephson junction using the RCSJ model for currents across the junction and includes surface resistance for currents along the junction. The travelling waves correspond to the so-called fluxons and their linear stability is determined by calculating the Evans function. Surface resistance corresponds to a singular perturbation term in the governing equation, which specifically complicates the computation of the corresponding Evans function. Both the flow of quasi-particles across and along the junction stabilise the waves.

    KW - METIS-211866

    KW - Evans function

    KW - IR-74894

    KW - Perturbed sine-Gordon equation

    KW - Travelling waves

    U2 - 10.1016/S0167-2789(03)00050-2

    DO - 10.1016/S0167-2789(03)00050-2

    M3 - Article

    VL - 180

    SP - 40

    EP - 70

    JO - Physica D

    JF - Physica D

    SN - 0167-2789

    IS - 1-2

    ER -