Dynamics of high-frequency modulated waves in a nonlinear dissipative continuous bi-inductance network

doi:10.1088/1674-1056/abd751

中国物理B ›› 2021, Vol. 30 ›› Issue (6): 60504-060504.doi: 10.1088/1674-1056/abd751

Dynamics of high-frequency modulated waves in a nonlinear dissipative continuous bi-inductance network

S M Ngounou^1,2 and F B Pelap^1,†

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:2020-09-27 修回日期:2020-12-20 接受日期:2020-12-30 出版日期:2021-05-18 发布日期:2021-05-18
通讯作者: F B Pelap E-mail:fbpelap@yahoo.fr

Dynamics of high-frequency modulated waves in a nonlinear dissipative continuous bi-inductance network

S M Ngounou^1,2 and F B Pelap^1,†

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:2020-09-27 Revised:2020-12-20 Accepted:2020-12-30 Online:2021-05-18 Published:2021-05-18
Contact: F B Pelap E-mail:fbpelap@yahoo.fr

摘要/Abstract

摘要： This paper presents intensive investigation of dynamics of high frequency nonlinear modulated excitations in a damped bimodal lattice. The effects of the dissipation are considered through a linear dissipation coefficient whose evolution in terms of the carrier wave frequency is checked. There appears that the dissipation coefficient increases with the carrier wave frequency. In the linear limit and for high frequency waves, study of the asymptotic behavior of plane waves reveals the existence of two additional regions in the dispersion curve where the modulational phenomenon is observed compared to the lossless line. Based on the multiple scales method exploited in the continuum approximation using an appropriate decoupling ansatz for the voltage of the two different cells, it appears that the motion of modulated waves is described by a dissipative complex Ginzburg-Landau equation instead of a Korteweg-de Vries equation. We also show that this amplitude wave equation admits envelope and hole solitons in the high frequency mode. From basic sources, we design a programmable electronic generator of complex signals with desired characteristics, which delivers signals exploited as input waves for all our numerical simulations. These simulations are performed in the LTspice software that uses realistic components and give the results that corroborate perfectly our analytical predictions.

关键词: dissipative bi-inductance network, high-frequency mode, continuous approximation, dissipative complex Ginzburg-Landau equation, programmable electronic generator, LT-Pspice observations

Abstract: This paper presents intensive investigation of dynamics of high frequency nonlinear modulated excitations in a damped bimodal lattice. The effects of the dissipation are considered through a linear dissipation coefficient whose evolution in terms of the carrier wave frequency is checked. There appears that the dissipation coefficient increases with the carrier wave frequency. In the linear limit and for high frequency waves, study of the asymptotic behavior of plane waves reveals the existence of two additional regions in the dispersion curve where the modulational phenomenon is observed compared to the lossless line. Based on the multiple scales method exploited in the continuum approximation using an appropriate decoupling ansatz for the voltage of the two different cells, it appears that the motion of modulated waves is described by a dissipative complex Ginzburg-Landau equation instead of a Korteweg-de Vries equation. We also show that this amplitude wave equation admits envelope and hole solitons in the high frequency mode. From basic sources, we design a programmable electronic generator of complex signals with desired characteristics, which delivers signals exploited as input waves for all our numerical simulations. These simulations are performed in the LTspice software that uses realistic components and give the results that corroborate perfectly our analytical predictions.

Key words: dissipative bi-inductance network, high-frequency mode, continuous approximation, dissipative complex Ginzburg-Landau equation, programmable electronic generator, LT-Pspice observations

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Yv (Solitons)

S M Ngounou and F B Pelap. Dynamics of high-frequency modulated waves in a nonlinear dissipative continuous bi-inductance network[J]. 中国物理B, 2021, 30(6): 60504-060504.

S M Ngounou and F B Pelap. Dynamics of high-frequency modulated waves in a nonlinear dissipative continuous bi-inductance network[J]. Chin. Phys. B, 2021, 30(6): 60504-060504.

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Dynamics of high-frequency modulated waves in a nonlinear dissipative continuous bi-inductance network

Dynamics of high-frequency modulated waves in a nonlinear dissipative continuous bi-inductance network

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