The propagation of the kink along the curved Josephson junction is considered. It is shown that the torsion as well as curvature is responsible for the existence of the energy barrier that affects the motion of the fluxon in the junction. It is also observed that the motion of the kink in the junction can be controlled in a very simple way even in the straight junction by modulating its width.
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Tomasz Dobrowolski (2009) studied this question.