Abstract
For the magnetically coupled waveguide and long Josephson junction we gave the analytic description of two separate velocity domains where the free motion of traveling vortex (2 π-kink) exists. The role of the mutual influence of waveguide and long Josephson junction is discussed. It is shown the possibility of the fast vortex motion with the velocity much larger than Swihart velocity of Josephson junction and close to the speed of light in the waveguide. The excitation of motion of such fast Josephson vortex is described.
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