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

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

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.

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  • [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.