Abstract
Nonlinear dynamics of vortices in high- J c overdamped Josephson contacts with time-dependent transport current J( t) is considered. It is shown that equations of nonlocal Josephson electrodynamics which describe an Abrikosov vortex with Josephson core can be solved exactly for any J( t). Different nonlinear regimes, such as vortex acceleration after a stepwise change of J( t) and oscillations of a vortex for periodic AC currents are calculated analytically.
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