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On the Continuous Generalized Solutions of a Lossless Transmission Line System with Josephson Junction

Year 2018, Volume: 1 Issue: 1, 30 - 45, 25.04.2018

Ljubomir P. Georgiev

Abstract

The present paper is devoted to the investigation of lossless transmission lines with Josephson junction. Such lines are described by first order nonlinear hyperbolic system partial differential equations. We consider the mixed problem for this system with boundary conditions generated by a circuit corresponding to Josephson junction formulated by V. Angelov. We present the mixed problem in an operator form and obtain a suitable sequence converging to a continuous solution.

Keywords

transmission lines Josephson junction nonlinear hyperbolic system mixed problem

References

  • [1] Scott A.C., F. Chu, S. Reible, Magnetic-flux propagation on a Josephson transmission line, J. Applied Physics v. 47, No. 7, July (1976), 3272–3286.
  • [2] Swihart J.C., Field solution for a thin-film superconducting strip transmission line, J. Applied Physics v. 32, No. 3, March (1961), 461–469.
  • [3] Barone A., G. Paterno, Physics and Applications of the Josephson Effect, A Wiley-Inter Science Publication, J. Wiley & Sons, New York, 1982.
  • [4] Cirillo M., Josephson Transmission Lines Coupling, in Nonlinear Superconductive Electronics and Josephson Devices, Proc. NATO Advanced Research Workshop on Nonlinear Superconductive Electronics and of the Second Workshop on Josephson Devices, (Ed: G. Costabile, S. Pagano, N.F. Pedersen, M. Russo), Springer Science+Business Media, NY, 1991, 297-305.
  • [5] V. G. Angelov, Lossless transmission lines with Josephson junction – approximated continuous generalized solutions, Journal of Multidisciplinary Engineering Science and Technology (JMEST) ISSN: 3159-0040 vol. 2 Issue 1 (2015), 291–298.
  • [6] Angelov V.G., Lossy Transmission Lines with Josephson Junction – Continuous Generalized Solutions. Communications in Applied Analysis 20 (2016), 91-106.
  • [7] Angelov V.G., Lossless Transmission Lines Terminated by L-Load in Series Connected to Parallel Connected GL-Loads. British Journal of Mathematics & Computer Science, 3 (3) (2013), 352-389.
  • [8] Angelov V.G., A Method for Analysis of Transmission Lines Terminated by Nonlinear Loads. Nova Science, New York, 2014.

Year 2018, Volume: 1 Issue: 1, 30 - 45, 25.04.2018

Ljubomir P. Georgiev

Abstract

References

  • [1] Scott A.C., F. Chu, S. Reible, Magnetic-flux propagation on a Josephson transmission line, J. Applied Physics v. 47, No. 7, July (1976), 3272–3286.
  • [2] Swihart J.C., Field solution for a thin-film superconducting strip transmission line, J. Applied Physics v. 32, No. 3, March (1961), 461–469.
  • [3] Barone A., G. Paterno, Physics and Applications of the Josephson Effect, A Wiley-Inter Science Publication, J. Wiley & Sons, New York, 1982.
  • [4] Cirillo M., Josephson Transmission Lines Coupling, in Nonlinear Superconductive Electronics and Josephson Devices, Proc. NATO Advanced Research Workshop on Nonlinear Superconductive Electronics and of the Second Workshop on Josephson Devices, (Ed: G. Costabile, S. Pagano, N.F. Pedersen, M. Russo), Springer Science+Business Media, NY, 1991, 297-305.
  • [5] V. G. Angelov, Lossless transmission lines with Josephson junction – approximated continuous generalized solutions, Journal of Multidisciplinary Engineering Science and Technology (JMEST) ISSN: 3159-0040 vol. 2 Issue 1 (2015), 291–298.
  • [6] Angelov V.G., Lossy Transmission Lines with Josephson Junction – Continuous Generalized Solutions. Communications in Applied Analysis 20 (2016), 91-106.
  • [7] Angelov V.G., Lossless Transmission Lines Terminated by L-Load in Series Connected to Parallel Connected GL-Loads. British Journal of Mathematics & Computer Science, 3 (3) (2013), 352-389.
  • [8] Angelov V.G., A Method for Analysis of Transmission Lines Terminated by Nonlinear Loads. Nova Science, New York, 2014.
There are 8 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Ljubomir P. Georgiev This is me

Publication Date April 25, 2018
Published in Issue Year 2018 Volume: 1 Issue: 1

Cite

APA Georgiev, L. P. (2018). On the Continuous Generalized Solutions of a Lossless Transmission Line System with Josephson Junction. Results in Nonlinear Analysis, 1(1), 30-45.
AMA Georgiev LP. On the Continuous Generalized Solutions of a Lossless Transmission Line System with Josephson Junction. RNA. April 2018;1(1):30-45.
Chicago Georgiev, Ljubomir P. “On the Continuous Generalized Solutions of a Lossless Transmission Line System With Josephson Junction”. Results in Nonlinear Analysis 1, no. 1 (April 2018): 30-45.
EndNote Georgiev LP (April 1, 2018) On the Continuous Generalized Solutions of a Lossless Transmission Line System with Josephson Junction. Results in Nonlinear Analysis 1 1 30–45.
IEEE L. P. Georgiev, “On the Continuous Generalized Solutions of a Lossless Transmission Line System with Josephson Junction”, RNA, vol. 1, no. 1, pp. 30–45, 2018.
ISNAD Georgiev, Ljubomir P. “On the Continuous Generalized Solutions of a Lossless Transmission Line System With Josephson Junction”. Results in Nonlinear Analysis 1/1 (April 2018), 30-45.
JAMA Georgiev LP. On the Continuous Generalized Solutions of a Lossless Transmission Line System with Josephson Junction. RNA. 2018;1:30–45.
MLA Georgiev, Ljubomir P. “On the Continuous Generalized Solutions of a Lossless Transmission Line System With Josephson Junction”. Results in Nonlinear Analysis, vol. 1, no. 1, 2018, pp. 30-45.
Vancouver Georgiev LP. On the Continuous Generalized Solutions of a Lossless Transmission Line System with Josephson Junction. RNA. 2018;1(1):30-45.
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