Alternate backward and forward waves in a coupled nonlinear transmission line

Ndecfo, Jean Emac; Deffo, Guy Roger; Yamgoué, Serge Bruno; Pelap, F. B.

doi:10.1140/epjp/s13360-019-00080-5

“…The nonlinear capacitor can be in the form of Toda lattice [13][14][15][16][17][18][19][20] or its expression can be obtained from the Taylor expansion of an experimentally double exponential form [21]. In that case, the nonlinear capacitance of the diode varactor has an asymmetric quadratic expression as in the low voltages reversebiased diode [22][23][24][25][26][27]. The choice of charge here is motivated by the recent development of strongly nonlinear and voltage symmetric barium strontium titanate thin film capacitors and the charge along the capacitance is given in the following [29,30]: .…”

Section: Model Descriptionmentioning

confidence: 99%

“…In the case where the nonlinear capacitance is the voltages reverse-biased diode, its expression has an asymmetric quadratic expression as in refs. [22][23][24][25][26][27].…”

mentioning

confidence: 99%

Travelling waves in discrete electrical lattice with nonlinear symmetric capacitor

Motcheyo

¹

,

Fezeu

²

,

Siewe

³

et al. 2022

Preprint

0

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We study the propagation of voltage in a model of the conventional right-handed transmission line with a nonlinear symmetric capacitor. Applying the quasidiscrete approximation to the nonlinear voltage equation of the line, we derive a nonlinear Schrödinger equation and find the bright and dark solutions which are used as the initial condition for the integration of the nonlinear lattice model. The full integration of the lattice shows the propagation of the nonlinear voltage in the right-hand side and its robustness in the time. The density energy of the lattice at each time has a node around which bright voltage is localized while in the case of dark voltage, it has a node where it seems to drop to zero at the soliton centre.

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“…The nonlinear capacitor can be in the form of Toda lattice [13][14][15][16][17][18][19][20] or its expression can be obtained from the Taylor expansion of an experimentally double exponential form [21]. In that case, the nonlinear capacitance of the diode varactor has an asymmetric quadratic expression as in the low voltages reversebiased diode [22][23][24][25][26][27]. The choice of charge here is motivated by the recent development of strongly nonlinear and voltage symmetric barium strontium titanate thin film capacitors and the charge along the capacitance is given in the following [29,30]: .…”

Section: Model Descriptionmentioning

confidence: 99%

“…In the case where the nonlinear capacitance is the voltages reverse-biased diode, its expression has an asymmetric quadratic expression as in refs. [22][23][24][25][26][27].…”

mentioning

confidence: 99%

Travelling waves in discrete electrical lattice with nonlinear symmetric capacitor

Motcheyo¹,

Fezeu

²

,

Siewe

³

et al. 2022

J Comput Electron

1

0

View full text Add to dashboard Cite

We study the propagation of voltage in a model of the conventional right-handed transmission line with a nonlinear symmetric capacitor. Applying the quasidiscrete approximation to the nonlinear voltage equation of the line, we derive a nonlinear Schrödinger equation and find the bright and dark solutions which are used as the initial condition for the integration of the nonlinear lattice model. The full integration of the lattice shows the propagation of the nonlinear voltage in the right-hand side and its robustness in the time. The density energy of the lattice at each time has a node around which bright voltage is localized while in the case of dark voltage, it has a node where it seems to drop to zero at the soliton centre.

show abstract

“…However, only a few scientific works linked to an analytical study of the propagation of modulated waves such as solitary waves or rogue waves in electrical transmission lines in at least one dimension with dissipative elements have been carried out. Classes of nonlinear Schrödinger equations have been used with the perturbation technique in different systems, such as studies on the formation and propagation of single rogue waves in a coupled distributed electrical transmission line [4], backward and forward wave propagation in a two-dimensional nonlinear transmission line [21], and soliton interactions in a nonlinear transmission line formed by several coupled Noguchi electric transmission lines [5]. More recently, some results have been obtained in the study of the formation and propagation of envelope solitons in a twodimensional nonlinear transmission line by deriving a modified ZakharovKuznetsov (ZK) equation in two dimensions by [22], the dynamics of modulated waves in a two-dimensional nonlinear discrete electrical transmission line composed of several Noguchi lines anharmonically modified by [23].…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of the effects of dissipative elements and modulational instability in a multicoupled nonlinear electrical transmission line with the propagation of new rogue waveforms

Ahmadou,

Alphonse,

Justin

et al. 2023

Phys. Scr.

0

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In this study, we consider a nonlinear multicoupled discrete electrical transmission line consisting of several modified Noguchi lines and analyze the dynamics of the effects of dissipative elements on modulated waves. This analysis shows that the dispersion element (C S ) and solution parameter (γ) strongly contribute to the increase in voltage amplitudes and to the modulation of these new rogue waveforms, unlike the dissipative element (G). Using a semi-discrete approximation, we demonstrate that the dynamics of modulated waves in such a dissipative electrical system can be governed by a system of nonlinear Schrödinger equations, the Manakov system, and system parameters. The phenomenon of modulational instability in this dissipative electrical system is studied, and areas of instability are shown. We found that the dissipative element of this system increased and decreased the areas of instability. Under the condition of this Manakov system, we determine the approximate modulated wave solutions that are then used for the dynamic analysis of the effects of dissipative elements when transmitting these new rogue waveforms through this dissipative electrical system. The effects of the parameters of this nonlinear dissipative electrical system, such as dispersive, dissipative, and solution parameters, in the dominant direction of propagation of these new rogue wave signals are presented. Based on these results, we observe that the effects of dissipative elements do exist in this nonlinear dissipative electrical system and that these dissipative elements would also impact the areas of modulational instability, which could gradually disappear in this electrical system.

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Alternate backward and forward waves in a coupled nonlinear transmission line

Cited by 9 publications

References 25 publications

Travelling waves in discrete electrical lattice with nonlinear symmetric capacitor

Travelling waves in discrete electrical lattice with nonlinear symmetric capacitor

Travelling waves in discrete electrical lattice with nonlinear symmetric capacitor

Dynamic analysis of the effects of dissipative elements and modulational instability in a multicoupled nonlinear electrical transmission line with the propagation of new rogue waveforms

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