Abstract
A generalization of the Sakai-Tateno-Pedersen model is proposed. This model is used to establish the existence of a discrete eigenvalue spectrum of the free-motion velocities of a Josephson vortex, or π kink, produced by the Cherenkov structure of extraordinary vortex-trapped Swihart waves having the spectrum (3.9). The dependence of the current across the Josephson junction on the vortex velocity was obtained, and, at comparatively high velocities, this was characterized by equidistant dips attributable to the Cherenkov resonant interaction of the vortex with Swihart waves.
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