2D Josephson junction

The paper is devoted to the determination of processes in the two-dimensional Josephson junction via numerical solution of 2+1 dimensional sine-Gordon equation (sGe) with suitably chosen boundary conditions. There is adopted an assumption that the normal derivative of the phase order parameter on a border of a junction is given by the surface current distribution on superconductive electrodes. This current distribution can be determined exactly since it makes a linear problem even in a presence of an external magnetic field although the surface current distribution is not uniform and can be singular. A rectangular junction is discussed as an example.