Approximations to large amplitude solitary waves on nonlinear electrical lattices

Hicks, A. C.; Common, A. K.; Sobhy, Mohammed

doi:10.1016/0167-2789(96)00038-3

Cited by 22 publications

(10 citation statements)

References 17 publications

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“…where C 0 and V 0 are arbitrary capacitance and voltage scales, respectively, and p > 0. Similar forms for C(V ) have been used in the past to model the capacitance of certain varactor diodes as part of comparisons with experimental measurements of solitary waves in NTL's [3]. Substituting (2.5) into (2.4), we find…”

Section: Electrical Modelsmentioning

confidence: 91%

Ginzburg–Landau system of complex modulation equations for a distributed nonlinear-dispersive transmission line

Kengne¹

2004

J. Phys. A: Math. Gen.

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The envelope modulation of a monoinductance transmission line is reduced to generalized coupled Ginzburg-Landau equations from which is deduced a single cubic-quintic Ginzburg-Landau equation containing derivatives with respect to the spatial variable in the cubic terms. We investigate the modulational instability of the spatial wave solutions of both the system and the single equation. For the generalized coupled Ginzburg-Landau system we consider only the zero wavenumbers of the perturbations whose modulational instability conditions depend only on the system's coefficients and the wavenumbers of the carriers. In this case, a modulational instability criterion is established which depends both on the perturbation wavenumbers and the carrier. We also study the coherent structures of the generalized coupled Ginzburg-Landau system and present some numerical studies. Огортуючу модуляцiю моноiндуктивної лiнiї передач зведено до узагальнених пов'язаних мiж собою рiвнянь Гiнзбурга-Ландау, звiдки отримано одне рiвняння Гiнзбурга-Ландау третьогоп'ятого порядку, яке мiстить похiднi вiдносно просторової змiнної в кубiчних членах. Для системи та рiвняння дослiджено модуляцiйну нестiйкiсть розв'язкiв у формi просторової хвилi. Для системи Гiнзбурга-Ландау розглянуто лише збурення з нульовими хвильовими числами, для яких умови модуляцiйної нестiйкостi залежать тiльки вiд коефiцiєнтiв системи та хвильових чисел носiїв. У цьому випадку отримано критерiй для модуляцiйної нестiйкостi, який залежить як вiд хвильових чисел збурень, так i вiд носiя. Також вивчаються когерентнi структури системи Гiнзбурга-Ландау та проведено деякий числовий аналiз.

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Section: Electrical Modelsmentioning

confidence: 91%

Ginzburg–Landau system of complex modulation equations for a distributed nonlinear-dispersive transmission line

Kengne¹

2004

J. Phys. A: Math. Gen.

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“…Similar forms for C(V ) have been used in the past for modeling the capacitance of certain varactor diodes as a part of comparisons with experimental measurements of solitary waves in nonlinear transmission lines [3]. Substituting (2.5) into (2.4), we find…”

Section: Electrical Modelsmentioning

confidence: 94%

Ginzburg-Landau system of complex modulation equations for distributed nonlinear dissipative transmission lines

Kengne

Vaillancourt

2006

Nonlinear Oscill

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The envelope modulation of a monoinductance transmission line is reduced to generalized coupled Ginzburg-Landau equations, from which a single cubic-quintic Ginzburg-Landau equation containing derivatives with respect to the space variable in the cubic terms is deduced. We investigate the modulational instability of the space wave solutions of both the system and the single equation. For the generalized coupled Ginzburg-Landau system, we consider only the zero wave numbers of the perturbations whose modulational instability conditions depend only on the coefficients of the system and the wave numbers of the carriers. In this case, a modulational instability criterion is established, which depends on both the perturbation wave numbers and the carrier. We also study the coherent structures of the generalized coupled Ginzburg-Landau system and present some numerical results.

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“…Similar forms for C(V ) have been used in the past to model the capacitance of certain varactor diodes as a part of comparisons with experimental measurements of solitary waves on NLT's [32]. Similar forms for C(V ) have been used in the past to model the capacitance of certain varactor diodes as a part of comparisons with experimental measurements of solitary waves on NLT's [32].…”

Section: Circuit Equationsmentioning

confidence: 99%

Dynamics of Modulated Wave Trains in a Discrete Nonlinear-dispersive Dissipative Bi-inductance Transmission Line

Kengne

Bame

2005

Czech J Phys

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In this paper nonlinear-dispersive dissipative RLC transmission line is considered and envelope modulation is reduced to the modified cubic-quintic complex Ginzburg-Landau equation (CGLE) with derivatives in cubic terms. This CGLE obtained contains two free (from the line parameters) parameters, the nonlinear cubic gain and the linear gain. Modulational instability for the modified cubic-quintic CGLE is analyzed and leads to the generalized Lange and Newell criterion. We reformulate the derived CGLE as a third-order ordinary system in standard form with the first derivatives on the left-hand side in order to study the coherent structures. PACS : 84.40.Az, 05.45.-a, 02.30.Jr

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Approximations to large amplitude solitary waves on nonlinear electrical lattices

Cited by 22 publications

References 17 publications

Ginzburg–Landau system of complex modulation equations for a distributed nonlinear-dispersive transmission line

Ginzburg–Landau system of complex modulation equations for a distributed nonlinear-dispersive transmission line

Ginzburg-Landau system of complex modulation equations for distributed nonlinear dissipative transmission lines

Dynamics of Modulated Wave Trains in a Discrete Nonlinear-dispersive Dissipative Bi-inductance Transmission Line

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