Nonlinear viscous motion of vortices in Josephson contacts

Nonlinear dynamics of vortices in current-carrying long Josephson contacts is considered for the cases of weak (${\lambda }_{\mathit{J}}$≫λ) and strong (${\lambda }_{\mathit{J}}$≪λ) couplings, where ${\lambda }_{\mathit{J}}$ and λ are the Josephson and London penetration depths, respectively. The first case concerns the Josephson vortices described by the sine-Gordon equation, whereas the case ${\lambda }_{\mathit{J}}$≪λ corresponds to Abrikosov-like vortices with highly anisotropic Josephson cores which are described by an integral equation for the phase difference cphi within the framework of a nonlocal Josephson electrodynamics. At ${\lambda }_{\mathit{J}}$≪λ, an exact solution for the moving vortex in the overdamped regime is obtained, the fluxon velocity v(j) and the voltage-current characteristic V(j) are calculated. It is shown that the lack of the Lorentz invariance of the integral equation for cphi in the nonlocal regime leads to specific features of the vortex dynamics as compared to the Josephson vortices. The results obtained are employed for the description of nonlinear viscous motion of magnetic flux along planar crystalline defects in superconductors. It is shown that any percolating network of planar defects can considerably reduce the critical current, change the field dependence of the flux-flow resistivity, and result in a nonlinear V(j) in the flux-flow regime.