Stability and Bifurcation of the Magnetic Flux Bound States in Stacked Josephson Junctions

The static distributions of the magnetic flux in stacked Josephson junctions are investigated numerically. To solve the nonlinear boundary value problem an iterative algorithm, based on the Continuous analog of Newton method is constructed. The linearized problems at every iteration step are solved by the Galerkin finite element method. In order to study the stability of possible distributions a Sturm-Liouville problem is generated. A minimal eigenvalue equal to zero means a bifurcation of the corresponding solution. The subspace iteration method is used to find the smallest eigenvalues and the corresponding eigenvectors.

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