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Stability analysis of p-kinks in a 0-p Josephson junction

Derks, Gianne, Doelman, A., van Gils, S. A. and Susanto, H. (2007) Stability analysis of p-kinks in a 0-p Josephson junction SIAM Journal on Applied Dynamical Systems, 6 (1). pp. 99-141.


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We consider a spatially nonautonomous discrete sine-Gordon equation with constant forcing and its continuum limit(s) to model a 0-pi Josephson junction with an applied bias current. The continuum limits correspond to the strong coupling limit of the discrete system. The nonautonomous character is due to the presence of a discontinuity point, namely, a jump of pi in the sine- Gordon phase. The continuum model admits static solitary waves which are called pi-kinks and are attached to the discontinuity point. For small forcing, there are three types of pi-kinks. We show that one of the kinks is stable and the others are unstable. There is a critical value of the forcing beyond which all static pi-kinks fail to exist. Up to this value, the (in)stability of the pi-kinks can be established analytically in the strong coupling limits. Applying a forcing above the critical value causes the nucleation of 2pi-kinks and -antikinks. Besides a pi-kink, the unforced system also admits a static 3pi-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 pi-kink remains stable and that the unstable pi-kinks cannot be stabilized by decreasing the coupling. The 3pi-kink does become stable in the discrete model when the coupling is sufficiently weak.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Doelman, A.
van Gils, S. A.
Susanto, H.
Date : 15 March 2007
DOI : 10.1137/060657984
Uncontrolled Keywords : 0-pi Josephson junction, 0-pi sine-Gordon equation, semifluxon, pi-kink
Additional Information : Published in the SIAM Journal of Applied and Dynamical Systems, 6, 99-141. © 2007, Society for Industrial and Applied Mathematics.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:41
Last Modified : 06 Jul 2019 05:07

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