Kink motion in a curved Josephson junction

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    Abstract

    The sine-Gordon equation is one of the three classical nonlinear partial differential equations possessing soliton solutions in the case of one spatial dimension. Extending the sine-Gordon equation to two spatial dimensions is relevant for applications to the dynamics of large area Josephson junctions. In particular we have investigated Josephson waveguides consisting of two rectangular large area regions joined by a bent section of constant curvature. Transverse homogeneous and inhomogeneous Neumann boundary conditions are used. Numerical and approximate analytical tools have been used to investigate how kink shaped solitons of the sine-Gordon equation propagate through the bent section. We have found that the region with finite curvature acts as a potential barrier whose height and width depends on the radius of curvature of the waveguide. The kink transmission, reflection and trapping is investigated. The kink may be captured when a driving force, provided by a magnetic field, is applied to the kink. The approximate analytical tools are based on a variational approach of a Lagrangian. The variation is done with respect to collective coordinates, or slowly varying coefficients, in the 1D soliton solution.
    Original languageEnglish
    Publication date2004
    Publication statusPublished - 2004
    EventSIAM Nonlinear Waves and Coherent Structures : October 2-5, 2004 - Orlando, Florida, USA
    Duration: 1 Jan 2004 → …

    Conference

    ConferenceSIAM Nonlinear Waves and Coherent Structures : October 2-5, 2004
    CityOrlando, Florida, USA
    Period01/01/2004 → …

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