Envelope solitons in a left-handed nonlinear transmission line with Josephson junction

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• 作者：Saidou Abdoulkary^a ; ^b ; ^c ; L.Q. English ; ^b ; ^{englishl@dickinson.edu" class="auth_mail" title="E-mail the corresponding author} ; Alidou Mohamadou^d ; ^c ; ^e
• 关键词：Josephson junction ; Left-handed transmission line ; Envelope soliton
• 刊名：Chaos, Solitons & Fractals
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：85
• 期：Complete
• 页码：44-50
• 全文大小：1410 K

文摘

We consider a nonlinear left-handed transmission line that incorporates an array of Josephson junctions in its periodic lattice structure. We show that the system dynamics is described by a discrete sine-Gordon-like equation, where the left-handedness of the lattice manifests in the form of a non-standard second-time- derivative term. Since this modified discrete sine-Gordon equation has not yet been extensively studied in the literature, this paper opens up the possibility of additional mathematical analysis. It is also intriguing that by means of a semi-discrete approximation we can derive a nonlinear Schrödinger equation and thus show that the system supports both bright and dark envelope soliton solutions depending on the choice of carrier frequency. The left-handedness of the network is explicitly confirmed in numerical simulations which demonstrate the backward propagation of the bright and dark soliton, in good agreement with analytical predictions.