The curved Josephson junction is described. In the framework of the Maxwell equations the equation that describes the influence of the curvature on the fluxion motion was obtained. The method of geometrical reduction of the sine-Gordon model from three to lower dimensional manifold was applied to the long Josephson junction. It was argued that the geometrical reduction describes the junctions with slowly varying curvatures.
Tomasz Dobrowolski. "The Fluxion in a Curved Josephson Junction." J. Geom. Symmetry Phys. 34 13 - 26, 2014. https://doi.org/10.7546/jgsp-34-2014-13-26