Numerical Investigation of a Bifurcation Problem with free Boundaries   Arising from the Physics of Josephson Junctions
  A direct method for calculating the minimal length of ``one-dimensional'' Josephson junctions is proposed, in which the specific distribution of the magnetic flux retains its stability. Since the length of the junctions is a variable quantity, the corresponding nonlinear spectral problem as a problem with free boundaries is interpreted. The obtained results give us warranty to consider as ``long'', every Josephson junction in which there exists at least one nontrivial stable distribution of the magnetic flux for fixed values of all other parameters. 
M. D. Todorov, T. L. Boyadjiev