Transverse stability of solitary waves propagating in coupled nonlinear dispersive transmission lines

Kengne, Emmanuel; Bozic, Vladan; Viana, Marcelo; Vaillancourt, Rémi

doi:10.1103/physreve.78.026603

Cited by 17 publications

(3 citation statements)

References 24 publications

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“…In the network, nonlinearity is introduced by a varicap diode which admits that the capacitance varies with the applied voltage. The voltage V n m , and the nonlinear electrical charge Q n m , at the ( ) n m th , are related by the polynomial form given by [53][54][55]:…”

Section: Model Description and Circuit Equations 21 Model Presentationmentioning

confidence: 99%

Hybrid behavior of a two-dimensional Noguchi nonlinear electrical network

2021

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In this work, the propagation of modulated waves in a nonlinear two-dimensional discrete electrical line is studied. Based on the linear dispersive law, we demonstrate that the network can adopt Hybrid’s behavior due to the fact that, without changing its appearance structure or its parameters values, it can become alternatively, a purely right-handed line, a purely left-handed line or a composite right-left-handed line depending on coupling transverse parameters L 2 , C 2 and k 2 . Using the reductive perturbation method, a (2+1)-dimensional nonlinear Schrodinger equation governing the dynamics of the small amplitude signals in the network is derived and the impact of the above transverse parameters on the sign of the product of their coefficients is examined. Likewise, backward and forward solitary wave propagations in the system is predicted and analyzed quantitatively and qualitatively. The effects of relevant transverse network parameters on the characteristic parameters of these waves are investigated. We find out that these transverse parameters considerably affect the characteristics and the nature of the waves that are propagated throughout the system.

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Section: Model Description and Circuit Equations 21 Model Presentationmentioning

confidence: 99%

Hybrid behavior of a two-dimensional Noguchi nonlinear electrical network

2021

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“…There have been particular applications of the KdV equations [10,11] and nonlinear Schrodinger equations [12,13]. Experiments have been performed on cylindrical solitons for a two-dimensional transmission line [14].…”

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confidence: 99%

2D Ginzburg-Landau System of Complex Modulation for Coupled Nonlinear Transmission Lines

Kengne

Vaillancourt

2009

J Infrared Milli Terahz Waves

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In this paper a coupled mono-inductance transmission line is considered and the envelope modulation is reduced to the generalized 2D-Ginzburg-Landau system (2D-GL system). The case of scalar equation is also considered and we deduce from the obtained 2D-GL system a 2D-cubic Ginzburg-Landau equation (2D-GL equation) containing the derivatives with respect to one spatial variable in the cubic terms. The obtained 2D-GL system and 2D-GL equation admit spatial wave solutions. The modulational instability of these spatial wave solutions is investigated. In the case of the 2D-GL system we have restricted ourselves in the zero wavenumber of the perturbations, and the obtained modulational instability conditions depends only on the system's coefficients and the wavenumber of the carriers. The modulational instability criterion is established for non zero wavenumber of the perturbation, and depends on both the wavenumber of the perturbation and the carrier. For the 2D-GL system we also study the coherent structures and present some numerical studies.Keywords Coupled nonlinear transmission line · 2D-Ginzburg-Landau system of complex modulation · 2D-modulational instability · 2D-coherent structure PACS 42.65.Tg · 42.25.Bs · 84.40.Az · 02.60.Cb

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“…Like every nonlinear system, a NLTL can exhibit an instability that leads to a self-induced modulation of input plane wave with the subsequence generation of localized pulses [16][17][18][19]. This phenomenon is known as a Benjamin-Feir modulational instability [20] and it is responsible of many physically interesting effects such as the formation of envelope solitons.…”

Section: Introductionmentioning

confidence: 99%

Dissipative Discrete System with Nearest-Neighbor Interaction for the Nonlinear Electrical Lattice

Abdoulkary¹,

Béda²,

Doka³

et al. 2012

JMP

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A generalized dissipative discrete complex Ginzburg-Landau equation that governs the wave propagation in dissipative discrete nonlinear electrical transmission line with negative nonlinear resistance is derived. This equation presents arbitrarily nearest-neighbor nonlinearities. We analyze the properties of such model both in connection to their modulational stability, as well as in regard to the generation of intrinsic localized modes. We present a generalized discrete Lange-Newell criterion. Numerical simulations are performed and we show that discrete breathers are generated through modulational instability.

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Transverse stability of solitary waves propagating in coupled nonlinear dispersive transmission lines

Cited by 17 publications

References 24 publications

Hybrid behavior of a two-dimensional Noguchi nonlinear electrical network

Hybrid behavior of a two-dimensional Noguchi nonlinear electrical network

2D Ginzburg-Landau System of Complex Modulation for Coupled Nonlinear Transmission Lines

Dissipative Discrete System with Nearest-Neighbor Interaction for the Nonlinear Electrical Lattice

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