Common features of vortex structure in long exponentially shaped   Josephson junctions and Josephson junctions with inhomogeneities
  We study vortex structure in three different models of long Josephson junctions: exponentially shaped Josephson junction and Josephson junctions with resistor and shunt inhomogeneities in barrier layer. Numerical calculations of the possible magnetic flux distributions and corresponding bifurcation curves have done. For these three models the critical curves ``critical current-magnetic field'' are constructed. We develop an idea of the equivalence of exponentially shaped Josephson junction and rectangular junction with distributed inhomogeneity and demonstrate that at some parameters of shunt and resistor inhomogeneities at the ends of the junction the corresponding critical curves are very close to the exponentially shaped one. 
T. L. Boyadjiev, E. G. Semerdjieva, Yu. M. Shukrinov