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

    16 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

    Keywords

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

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