Coordinate transformation in the model of long Josephson contacts: geometrically equivalent contacts

The transition from model of long Josephson variable-width contact to the contact model with coordinate-dependent Josephson current amplitude is realized by transforming the coordinates. This sets up a correspondence between Josephson contacts of variable width and quasi-one-dimensional contacts of variable thickness barrier layer. It is shown, that for contacts of exponentially varying width the barrier layer of the corresponding quasi-one-dimensional contact contains the distributed resistive inhomogeneity which is an attractor to magnetic flux vortices. With numerical experiments, a 'critical current-magnetic field' dependence for a resistive microinhomogeneity Josephson contact was plotted, and its comparison with the critical curve for a contact of exponentially varying width was made. Thus, this demonstrates that the distributed inhomogeneity may be replaced by a local one at the JC end what technologically, may offer definite advantages