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Existence, uniqueness and multiplicity of rotating fluxon waves in annular Josephson junctions. (English) Zbl 1212.35418

Summary: We prove that the equation modelling an annular Josephson junction has a rotating fluxon wave solution for all values of the parameters. We also obtain results on uniqueness of the rotating fluxon wave in some parameter regimes, and on multiplicity of rotating fluxon waves in other parameter regimes.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B10 Periodic solutions to PDEs
35B35 Stability in context of PDEs
82D55 Statistical mechanics of superconductors
47J05 Equations involving nonlinear operators (general)
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