Nonlinear continuous bi-inductance electrical line with dissipative elements: Dynamics of the low frequency modulated waves

doi:10.1088/1674-1056/ab75d6

中国物理B ›› 2020, Vol. 29 ›› Issue (4): 40502-040502.doi: 10.1088/1674-1056/ab75d6

Nonlinear continuous bi-inductance electrical line with dissipative elements: Dynamics of the low frequency modulated waves

S M Ngounou, F B Pelap

1 Unité de Recherche de Mécanique et de Modélisation des Systèmes Physiques(UR-2 MSP), Faculté des Sciences, Université de Dschang, BP 69 Dschang, Cameroun;
2 Unité de Recherche de Matière Condensée d'Electronique et de Traitement du Signal(UR-MACETS), Faculté des Sciences, Université de Dschang, BP 67 Dschang, Cameroun

收稿日期:2020-01-01 修回日期:2020-01-22 出版日期:2020-04-05 发布日期:2020-04-05
通讯作者: F B Pelap E-mail:fbpelap@yahoo.fr,francois.pelap@univ-dschang.org

Nonlinear continuous bi-inductance electrical line with dissipative elements: Dynamics of the low frequency modulated waves

S M Ngounou^1,2, F B Pelap¹

1 Unité de Recherche de Mécanique et de Modélisation des Systèmes Physiques(UR-2 MSP), Faculté des Sciences, Université de Dschang, BP 69 Dschang, Cameroun;
2 Unité de Recherche de Matière Condensée d'Electronique et de Traitement du Signal(UR-MACETS), Faculté des Sciences, Université de Dschang, BP 67 Dschang, Cameroun

Received:2020-01-01 Revised:2020-01-22 Online:2020-04-05 Published:2020-04-05
Contact: F B Pelap E-mail:fbpelap@yahoo.fr,francois.pelap@univ-dschang.org

摘要/Abstract

摘要： The dynamics of modulated waves in a nonlinear bi-inductance transmission line with dissipative elements are examined. We show the existence of two frequency modes and carry out intensive investigations on the low frequency mode. Thanks to the multiple scales method, the behavior of these waves is investigated and the dissipative effects are analyzed. It appears that the dissipation coefficient increases with the carrier wave frequency. In the continuous approximation, we derive that the propagation of these waves is governed by the complex Ginzburg-Landau equation instead of the Korteweg-de-Vries equation as previously established. Asymptotic studies of the dynamics of plane waves in the line reveal the existence of three additional regions in the dispersion curve where the modulational phenomenon is observed. In the low frequency mode, we demonstrate that the network allows the propagation of dark and bright solitons. Numerical findings are in perfect agreement with the analytical predictions.

关键词: dissipative bi-inductance network, low frequency mode, continuous approximation, complex Ginzburg-Landau equation

Abstract: The dynamics of modulated waves in a nonlinear bi-inductance transmission line with dissipative elements are examined. We show the existence of two frequency modes and carry out intensive investigations on the low frequency mode. Thanks to the multiple scales method, the behavior of these waves is investigated and the dissipative effects are analyzed. It appears that the dissipation coefficient increases with the carrier wave frequency. In the continuous approximation, we derive that the propagation of these waves is governed by the complex Ginzburg-Landau equation instead of the Korteweg-de-Vries equation as previously established. Asymptotic studies of the dynamics of plane waves in the line reveal the existence of three additional regions in the dispersion curve where the modulational phenomenon is observed. In the low frequency mode, we demonstrate that the network allows the propagation of dark and bright solitons. Numerical findings are in perfect agreement with the analytical predictions.

Key words: dissipative bi-inductance network, low frequency mode, continuous approximation, complex Ginzburg-Landau equation

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Yv (Solitons)

S M Ngounou, F B Pelap. Nonlinear continuous bi-inductance electrical line with dissipative elements: Dynamics of the low frequency modulated waves[J]. 中国物理B, 2020, 29(4): 40502-040502.

S M Ngounou, F B Pelap. Nonlinear continuous bi-inductance electrical line with dissipative elements: Dynamics of the low frequency modulated waves[J]. Chin. Phys. B, 2020, 29(4): 40502-040502.

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Nonlinear continuous bi-inductance electrical line with dissipative elements: Dynamics of the low frequency modulated waves

Nonlinear continuous bi-inductance electrical line with dissipative elements: Dynamics of the low frequency modulated waves

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