Exact Travelling Envelope Solitons and Kink-soliton Solutions for the Josephson Nonlinear Left-handed Transmission Line

Alphonse HOUWE^{1, 2,} , YERIMA KLOFAI³, Boudoue Hubert Malwe² and Serge Y. Doka^{3, 4}

¹Department of Marine engineering, Limbe Nautical Arts and Fisheries Institute, P.O. Box. 485 Limbe, Cameroon

²Department of Physics, Faculty of Science, University of Maroua, P.O. Box, 814, Maroua, Cameroon

³Department of Physics, Higher Teachers’ Training College, University of Maroua, P.O. Box, 55, Maroua, Cameroon

⁴Department of Physics, Faculty of Science, University of Ngaoundere, P.O. Box, 454, Ngaoundère, Cameroon

Cite this paper:
Alphonse HOUWE, YERIMA KLOFAI, Boudoue Hubert Malwe and Serge Y. Doka. Exact Travelling Envelope Solitons and Kink-soliton Solutions for the Josephson Nonlinear Left-handed Transmission Line. Applied Mathematics and Physics. 2017; 5(3):77-84. doi: 10.12691/amp-5-3-1

Abstract

Exact traveling soliton solutions for the Josephson nonlinear Left-handed transmission line (NL-JLHTL) based on the periodic structure of an array of Josephson junctions (JJs) are investigated. The nonlinearity of the Josephson left-handed transmission line (JLHTL) is due to the highly nonlinear nature of the JJs that provide the shunt inductances required to realize an LHTL. Applying the generalized Ricati methods, we analytically and successfully derive exact traveling kink solitons, bright and dark solitary wave solutions on this network. The left-handedness of the line is explicitly confirmed in numerical simulations with the existence of bright and dark soliton solutions in good agreement with analytical predictions.

Keywords:
Josephson nonlinear left-handed transmission line Josephson junction Envelope solitons and kink-soliton

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References:

[1]	H. Salehi, R.R. Mansour and A.H. Majedi, Nonlinear Josephson left-handed transmission lines, IET Microw. Antennas Propag., 2007, 1, (1), pp. 69-72.
[2]	K, Alan M., Introduction to superconducting circuits, New York: Wiley, c1999.
[3]	A. Barone, G. Paterno, “Physics and applications of the Josephson effect”, 2nd Edition, John Wiley & Sons, 1982.
[4]	McLaughlin DW, CScott A. Phys Rev A 1978;18: 1652.
[5]	Salehi H, Mansour RR, Majedi AH. IET Microwaves Antennas & Propagation 2007; 1: 69.
[6]	Collin RE. Field Theory of Guided Waves. Oxford: Oxford University Press; 1991.
[7]	A. Shahvarpour, S. Gupta, and C. Caloz, J. Appl. Phys. 104, 1245102008.
[8]	S. Gupta and C. Caloz, IEEE MTT-S Int. Microwaves Symp. Dig. 1,979 2007.
[9]	A. B. Kozyrev, and D.W. van der Weide, ‘Nonlinear wavepropagation phenomena in left-handed transmission-line media’, IEEE Trans. Microw. Theory Tech., 2005, 53, (1), pp. 238-245.
[10]	A. Barone, G. Paterno, “Physics and applications of the Josephson effect”, 2nd Edition, John Wiley & Sons, 1982.
[11]	B. H. Malwe, G. Betchewe,·S. Y. Doka, “Travelling wave solutions and soliton solutions for the nonlinear transmission line using the generalized Riccati equation mapping method”, Springer Science+Business Media Dordrecht 2015.
[12]	Shun-don, Z. “The generalizing Riccati equation map- ping method in non-linear evolution equation: application to (2+1)-dimensional Boiti–Leon–Pempinelle equation. Chaos Solitons Fract”. 37, 1335-1342 (2008).
[13]	Zheng, C.L. “Comment on the generalizing Riccati equation mapping method in nonlinear evolution equation: application to (2+1)-dimensionalBoiti–Leon–Pempinelle equation. Chaos Solitons Fract”. 39, 1493-1495 (2009).
[14]	L.Q. English, S.G. Wheeler, Y. Shen b, G.P. Veldes, N. Whitaker, P.G. Kevrekidis, D.J. Frantzeskakis, “Backward-wave propagation and discrete solitons in a left-handed electrical lattice”, Physics Letters A 375 (2011) 1242-1248, (2011).
[15]	S. Abdoulkary, L.Q. English, A. Mohamadoud, “Envelope solitons in a left-handed nonlinear transmission line with Josephson junction”, Chaos, Solitons and Fractals 85 (2016) 44-50, (2016).
[16]	Z. Wang, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “Dark Schrödinger solitons and harmonic generation in left-handed nonlinear transmission line”, Journal of Applied Physics 107, 094907 (2010).
[17]	S. ABDOULKARY and al, dynamics of solitary pulses in the nonlinear low-pass electrical transmission lines through the auxiliary equation method, J. Mod. Phys. Appl. 2 (2013).