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Exotic modulated signals in a nonlinear electrical transmission line: Modulated peak solitary wave and gray compacton

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  • Kenmogne, Fabien
  • Yemélé, David

Abstract

The dynamics of modulated signals in a nonlinear discrete electrical transmission line with the intersite nonlinearity is interpreted in terms of the extended nonlinear Schrödinger-type (ENLS) equation with nonlinear dispersion introduced by Yemele and Kenmogne (2009) [10]. We show that this ENLS equation may simplify as iAt+PAxx+Q∣A∣2A=ir1∣A∣2Ax+r23A∗(A2)xx+r3A(∣A2∣)xx and exhibits two branches of non smooth solutions according to the sign of the quantity μ2=(16r23Q-r12)/[64r23(r23+r3)]: a branch which contains a peak solitary wave when μ2>0 and another containing gray compacton for μ2<0. Exact analytical expressions for these solutions are derived as well as their properties, namely existence and stability. The exactness of this analytical analysis is confirmed by numerical simulations performed both on the ENLS equation and on the exact equations of the network. These solutions may have important applications in communication systems where solitons are used to codify data.

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  • Kenmogne, Fabien & Yemélé, David, 2012. "Exotic modulated signals in a nonlinear electrical transmission line: Modulated peak solitary wave and gray compacton," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 21-34.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:1:p:21-34
    DOI: 10.1016/j.chaos.2011.09.009
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    1. Kenmogne, Fabien & Wokwenmendam, Martine Limi & Simo, Hervé & Adile, Adoum Danao & Noah, Pierre Marcel Anicet & Barka, Mahamat & Nguiya, Sévérin, 2022. "Effects of damping on the dynamics of an electromechanical system consisting of mechanical network of discontinuous coupled system oscillators with irrational nonlinearities: Application to sand sieve," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

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