Magnetic vortices in a distributed Josephson junction with electrodes of finite thickness

A distributed Josephson junction with electrodes of finite thickness is considered in the case of high critical current density when the Josephson penetration depth ${\lambda }_{\mathit{j}}$ is less than the London depth ${\lambda }_{\mathit{L}}$. A nonlinear nonlocal equation for steady-state distributions of phase difference cphi across the junction is derived. In the asymptotical case of thin electrodes an exact nonlinear solution for this equation which corresponds to an isolated at-rest Josephson vortex is found. A numerical investigation of the equation derived is carried out and some static and dynamic characteristics of vortices in such a Josephson junction are represented.