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

Derks, G.
and
Doelman, A.
and
Gils, S.A. van
and
Susanto, H.
(2007)
*Stability analysis of -kinks in a 0- Josephson junction.*
SIAM Journal on Applied Dynamical Systems (SIADS), 6
(1).
pp. 99-141.
ISSN 1536-0040

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Abstract: | We consider a spatially nonautonomous discrete sine-Gordon equation with constant forcing and its continuum limit(s) to model a 0- 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 in the sine-Gordon phase. The continuum model admits static solitary waves which are called -kinks and are attached to the discontinuity point. For small forcing, there are three types of -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 -kinks fail to exist. Up to this value, the (in)stability of the -kinks can be established analytically in the strong coupling limits. Applying a forcing above the critical value causes the nucleation of 2-kinks and -antikinks. Besides a -kink, the unforced system also admits a static 3-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 -kink remains stable and that the unstable -kinks cannot be stabilized by decreasing the coupling. The 3-kink does become stable in the discrete model when the coupling is sufficiently weak. |

Item Type: | Article |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/62039 |

Official URL: | http://dx.doi.org/10.1137/060657984 |

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