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Dynamics of spatiotemporal modulated damped signals in a nonlinear RLC transmission network

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Abstract

The dynamics of spatiotemporal modulated damped signals in a nonlinear LC transmission network with dissipative elements are investigated analytically. The complex cubic Ginzburg–Landau (GL) equation governing slowly modulated wave propagation is presented. Considering linear wave propagating in the network, we derive in terms of the propagating frequency the spatial decreasing rate (linear dissipation parameter) and show that its must important contribution comes from the dissipative element of the shunt branch. The modulational instability (MI) criterion of modulated Stokes wave propagating in the network is investigated and the analytical expression of the MI growth rate is derived; we show that in the case of weak dissipation, there are no significant changes for the bandwidth frequency where the network may exhibit MI. Exact and approximative envelope soliton-like solutions of the derived GL equation are presented and used to investigate the dynamics of spatiotemporal modulated damped signals along the network. We show that the solution parameters can be used for managing the evolution of the envelope soliton signals along the network. Our investigation shows that the amplitude decays in both space (cell number n) and time t, while the velocity remains constant when the envelope soliton signal propagates along the dissipative network.

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Authors and Affiliations

  1. School of Physics and Electronic Information Engineering, Zhejiang Normal University, Jinhua, 321004, China

    Emmanuel Kengne

  2. Institut Universitaire de la Côte, Département de mathématiques, B.P 3001, Douala, Cameroun

    Elvis Benzo Ngompe Nkouankam

  3. Laboratory of Advanced Microsystems Engineering, Department of Computer Science and Engineering, University of Quebec at Outaouais, 101 St-Jean-Bosco, Succursale Hull, Gatineau, Quebec, J8Y 3G5, Canada

    Ahmed Lakhssassi

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  1. Emmanuel Kengne
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  2. Elvis Benzo Ngompe Nkouankam
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  3. Ahmed Lakhssassi
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Correspondence to Emmanuel Kengne.

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The first author, E. Kengne dedicates this work to his children, Kengneson Delma Djomo, Kengneson Weierstrass Owan Wambo, and Kengneson Cris-Carelle Djike, all living at Gatineau-Quebec, Canada.

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Kengne, E., Nkouankam, E.B.N. & Lakhssassi, A. Dynamics of spatiotemporal modulated damped signals in a nonlinear RLC transmission network. Nonlinear Dyn 104, 4181–4201 (2021). https://doi.org/10.1007/s11071-021-06466-4

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