### Abstract

Original language | Undefined |
---|---|

Article number | 10.1137/060657984 |

Pages (from-to) | 99-141 |

Number of pages | 43 |

Journal | SIAM journal on applied dynamical systems |

Volume | 6 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2007 |

### Keywords

- METIS-247074
- MSC-34D35
- EWI-11491
- MSC-35Q53
- MSC-37K50
- MSC-39A11
- IR-62039

### Cite this

*SIAM journal on applied dynamical systems*,

*6*(1), 99-141. [10.1137/060657984]. https://doi.org/10.1137/060657984

}

*SIAM journal on applied dynamical systems*, vol. 6, no. 1, 10.1137/060657984, pp. 99-141. https://doi.org/10.1137/060657984

**Stability analysis of π-kinks in a 0-π Josephson junction.** / Derks, G.; Doelman, A.; van Gils, Stephanus A.; Susanto, H.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Stability analysis of π-kinks in a 0-π Josephson junction

AU - Derks, G.

AU - Doelman, A.

AU - van Gils, Stephanus A.

AU - Susanto, H.

N1 - 10.1137/060657984

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - METIS-247074

KW - MSC-34D35

KW - EWI-11491

KW - MSC-35Q53

KW - MSC-37K50

KW - MSC-39A11

KW - IR-62039

U2 - 10.1137/060657984

DO - 10.1137/060657984

M3 - Article

VL - 6

SP - 99

EP - 141

JO - SIAM journal on applied dynamical systems

JF - SIAM journal on applied dynamical systems

SN - 1536-0040

IS - 1

M1 - 10.1137/060657984

ER -