### Abstract

A study is carried out of the sine-Gordon equation and systems of discrete approximations to it which are respectively a model of the Josephson junction and models of coupled-point Josephson junctions. The so-called current-drive case is considered. The voltage response of these devices is the average of the time derivative of the solution of these equations and the authors demonstrate the existence of running periodic solutions for which the average exists. Static solutions are also studied. These together with the running solutions explain the multiple-valuedness in the response of a Josephson junction in several cases. The stability of the various solutions is described in some of the cases. Numerical results are displayed which give details of structure of solution types in the case of a single point junction and of the one-dimensional distributed junction.

Original language | English (US) |
---|---|

Pages (from-to) | 167-198 |

Number of pages | 32 |

Journal | Quarterly of Applied Mathematics |

Volume | 36 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1978 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Applied Mathematics

### Cite this

*Quarterly of Applied Mathematics*,

*36*(2), 167-198. https://doi.org/10.1090/qam/484023

}

*Quarterly of Applied Mathematics*, vol. 36, no. 2, pp. 167-198. https://doi.org/10.1090/qam/484023

**DYNAMICS OF THE JOSEPHSON JUNCTION.** / Levi, Mark; Hoppensteadt, F. C.; Miranker, W. L.

Research output: Contribution to journal › Article

TY - JOUR

T1 - DYNAMICS OF THE JOSEPHSON JUNCTION.

AU - Levi, Mark

AU - Hoppensteadt, F. C.

AU - Miranker, W. L.

PY - 1978/1/1

Y1 - 1978/1/1

N2 - A study is carried out of the sine-Gordon equation and systems of discrete approximations to it which are respectively a model of the Josephson junction and models of coupled-point Josephson junctions. The so-called current-drive case is considered. The voltage response of these devices is the average of the time derivative of the solution of these equations and the authors demonstrate the existence of running periodic solutions for which the average exists. Static solutions are also studied. These together with the running solutions explain the multiple-valuedness in the response of a Josephson junction in several cases. The stability of the various solutions is described in some of the cases. Numerical results are displayed which give details of structure of solution types in the case of a single point junction and of the one-dimensional distributed junction.

AB - A study is carried out of the sine-Gordon equation and systems of discrete approximations to it which are respectively a model of the Josephson junction and models of coupled-point Josephson junctions. The so-called current-drive case is considered. The voltage response of these devices is the average of the time derivative of the solution of these equations and the authors demonstrate the existence of running periodic solutions for which the average exists. Static solutions are also studied. These together with the running solutions explain the multiple-valuedness in the response of a Josephson junction in several cases. The stability of the various solutions is described in some of the cases. Numerical results are displayed which give details of structure of solution types in the case of a single point junction and of the one-dimensional distributed junction.

UR - http://www.scopus.com/inward/record.url?scp=0017985657&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0017985657&partnerID=8YFLogxK

U2 - 10.1090/qam/484023

DO - 10.1090/qam/484023

M3 - Article

VL - 36

SP - 167

EP - 198

JO - Quarterly of Applied Mathematics

JF - Quarterly of Applied Mathematics

SN - 0033-569X

IS - 2

ER -