Stability analysis of $π$-kinks in a 0-$π$ Josephson junction

dc.creatorDerks, G.
dc.creatorDoelman, A.
dc.creatorvan Gils, S. A.
dc.creatorSusanto, H.
dc.date2008-01-22
dc.date.accessioned2026-07-07T08:55:51Z
dc.date.available2026-07-07T08:55:51Z
dc.descriptionWe consider a spatially non-autonomous discrete sine-Gordon equation with constant forcing and its continuum limit(s) to model a 0-$π$ Josephson junction with an applied bias current. The continuum limits correspond to the strong coupling limit of the discrete system. The non-autonomous character is due to the presence of a discontinuity point, namely a jump of $π$ in the sine-Gordon phase. The continuum models admits static solitary waves which are called $π$-kinks and are attached to the discontinuity point. For small forcing, there are three types of $π$-kinks. We show that one of the kinks is stable and the others are unstable. There is a critical value of the forcing beyond all static $π$-kinks fail to exist. Up to this value, the (in)stability of the $π$-kinks can be established analytically in the strong coupling limits. Applying a forcing above the critical value causes the nucleation of $2π$-kinks and -antikinks. Besides a $π$-kink, the unforced system also admits a static $3π$-kink. This state is unstable in the continuum models. By combining analytical and numerical methods in the discrete model, it is shown that the stable $π$-kink remains stable, and that the unstable $π$-kinks cannot be stabilized by decreasing the coupling. The $3π$-kink does become stable in the discrete model when the coupling is sufficiently weak.
dc.descriptionfigures are not included due to file size limit
dc.identifierhttps://arxiv.org/abs/0801.3398
dc.identifierhttp://arxiv.org/abs/0801.3398
dc.identifierSIAM J. Appl. Dyn. Syst. 6, 99-141 (2007)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146410
dc.subjectPattern Formation and Solitons
dc.subjectSuperconductivity
dc.titleStability analysis of $π$-kinks in a 0-$π$ Josephson junction
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