Kink propagation and trapping in a two-dimensional curved Josephson junction

Sine-Gordon kink propagation in a curved planar waveguide is considered. The waveguide consists of two rectangular regions joined by a bent section of constant curvature. Transverse homogeneous and inhomogeneous Neumann boundary conditions are used. The latter models an energy-providing mechanism for Josephson junctions of overlap type.

A collective variable approach based on the kink position and the kink width depending on the transversal coordinate is developed. The latter allows to take into account both longitudinal and centrifugal forces which act on the nonlinear excitation moving in a region with finite curvature and to obtain a qualitatively good agreement with the numerical simulations.

The region with finite curvature acts as a potential barrier whose height and width depend on the radius of curvature of the waveguide. The kink transmission, reflection, and trapping are investigated. The kink may be captured when a driving force, provided by a magnetic field, is applied to the kink.