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Stability Analysis of &#960-Kinks in a 0-&#960 Josephson Junction

Derks, G, Doelman, A, van Gils, S A and Susanto, H (2007) Stability Analysis of &#960-Kinks in a 0-&#960 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 2 pi-kinks and -antikinks. Besides a pi- kink, the unforced system also admits a static 3 pi-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 3 pi- 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 : 1 January 2007
DOI : 10.1137/060657984
Additional Information : Derks, G., Doelman, A., van Gils, S. A., and Susanto, H. (2007) Stability Analysis of &amp;#960-Kinks in a 0-&amp;#960 Josephson Junction, <i>SIAM Journal on Applied Dynamical Systems,</i> Vol. 6, No. 1, pp. 99-141. © 2007 Society for Industrial and Applied Mathematics. Click <a href= >here</a> to visit the journal's website.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:41
Last Modified : 16 Jan 2019 16:22

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