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faculty: "FNWI" and publication year: "2007"
| Authors||G. Derks, A. Doelman, S.A. van Gils, H. Susanto|
|Title||Stability Analysis of pi-Kinks in a 0-pi Josephson Junction|
|Journal||SIAM Journal on Applied Dynamical Systems|
|Faculty||Faculty of Science|
|Institute/dept.||FNWI: Korteweg-de Vries Institute for Mathematics (KdVI)|
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.
Keywords: 0-pi Josephson junction; 0-pi sine-Gordon equation; semifluxon; pi-kink|
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