  The transition from the model of a long Josephson junction of variable width
to the model of a junction with a coordinate-dependent Josephson current
amplitude is effected through a coordinate transformation. This establishes the
correspondence between the classes of Josephson junctions of variable width and
quasi-one-dimensional junctions with a variable thickness of the barrier layer.
It is shown that for a junction of exponentially varying width the barrier
layer of the equivalent quasi-one-dimensional junction has a distributed
resistive inhomogeneity that acts as an attractor for magnetic flux vortices.
The curve of the critical current versus magnetic field for a Josephson
junction with a resistive microinhomogeneity is constructed with the aid of a
numerical simulation, and a comparison is made with the critical curve of a
junction of exponentially varying width. The possibility of replacing a
distributed inhomogeneity in a Josephson junction by a local inhomogeneity at
the end of the junction is thereby demonstrated; this can have certain
advantages from a technological point of view.
