Stability analysis of pkinks in a 0p Josephson junction
Derks, Gianne, Doelman, A., van Gils, S. A. and Susanto, H. (2007) Stability analysis of pkinks in a 0p Josephson junction SIAM Journal on Applied Dynamical Systems, 6 (1). pp. 99141.

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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 sine Gordon 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 pikinks 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 2pikinks and antikinks. Besides a pikink, the unforced system also admits a static 3pikink. 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 3pikink 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 :  15 March 2007  
Identification Number :  10.1137/060657984  
Uncontrolled Keywords :  0pi Josephson junction, 0pi sineGordon equation, semifluxon, pikink  
Additional Information :  Published in the SIAM Journal of Applied and Dynamical Systems, 6, 99141. © 2007, Society for Industrial and Applied Mathematics.  
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/1491 
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