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The transition from the model of a long Josephson junction of variable widthto the model of a junction with a coordinate-dependent Josephson currentamplitude is effected through a coordinate transformation. This establishes thecorrespondence between the classes of Josephson junctions of variable width andquasi-one-dimensional junctions with a variable thickness of the barrier layer.It is shown that for a junction of exponentially varying width the barrierlayer of the equivalent quasi-one-dimensional junction has a distributedresistive inhomogeneity that acts as an attractor for magnetic flux vortices.The curve of the critical current versus magnetic field for a Josephsonjunction with a resistive microinhomogeneity is constructed with the aid of anumerical simulation, and a comparison is made with the critical curve of ajunction of exponentially varying width. The possibility of replacing adistributed inhomogeneity in a Josephson junction by a local inhomogeneity atthe end of the junction is thereby demonstrated; this can have certainadvantages from a technological point of view.

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