Abstract
We investigate analytically a long Josephson junction with several $\pi$-discontinuity points characterized by a jump of $\pi$ in the phase difference of the junction. The system is described by a perturbed-combined sine-Gordon equation. Via phase-portrait analysis, it is shown how the existence of static semifluxons localized around the discontinuity points is influenced by the applied bias current. In junctions with more than one corner, there is a minimum-facet-length for semifluxons to be spontaneously generated. A stability analysis is used to obtain the minimum-facet-length for multicorner junctions.
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