Stability Analysis of πKinks in a 0π Josephson Junction
Derks, G, Doelman, A, van Gils, S A and Susanto, H (2007) Stability Analysis of πKinks in a 0π Josephson Junction SIAM Journal on Applied Dynamical Systems, 6 (1). pp. 99141. ISSN 15360040

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Abstract
We consider a spatially nonautonomous discrete sineGordon equation with constant forcing and its continuum limit(s) to model a 0pi 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 sineGordon phase. The continuum model admits static solitary waves which are called pikinks and are attached to the discontinuity point. For small forcing, there are three types of pikinks. 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 pikinks can be established analytically in the strong coupling limits. Applying a forcing above the critical value causes the nucleation of 2 pikinks and antikinks. Besides a pi kink, the unforced system also admits a static 3 pikink. This state is unstable in the continuum models. By combining analytical and numerical methods in the discrete model, it is shown that the stable pikink remains stable and that the unstable pikinks 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 : 


Date :  1 January 2007  
Identification Number :  10.1137/060657984  
Additional Information :  Derks, G., Doelman, A., van Gils, S. A., and Susanto, H. (2007) Stability Analysis of &#960Kinks in a 0&#960 Josephson Junction, <i>SIAM Journal on Applied Dynamical Systems,</i> Vol. 6, No. 1, pp. 99141. © 2007 Society for Industrial and Applied Mathematics. Click <a href=http://epubs.siam.org/SIADS/siads_toc.html >here</a> to visit the journal's website.  
Depositing User :  Mr Adam Field  
Date Deposited :  27 May 2010 14:41  
Last Modified :  23 Sep 2013 18:33  
URI:  http://epubs.surrey.ac.uk/id/eprint/1490 
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