Backward-wave propagation and discrete solitons in a left-handed electrical lattice

English, Lars Q.; Wheeler, S. G.; Shen, Yong; Veldes, G. P.; Whitaker, N.; Kevrekidis, P. G.; Frantzeskakis, D. J.

doi:10.1016/j.physleta.2011.01.042

Cited by 60 publications

(57 citation statements)

References 32 publications

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“…Indeed, such nonlinear lattice models appear in the context of nonlinear lefthanded transmission line metamaterials and have been studied also in experiments (see, e.g. [Kozyrev & van der Weide, 2008;Ogaswara & Narahara, 2010;English et al, 2011]). In most of the relevant settings, the focus was on the reduction of the lattice model to an effective nonlinear Schrödinger (NLS) equation, by means of which approximate soliton solutions of the original model were presented.…”

Section: Resultsmentioning

confidence: 99%

Bifurcation Results for Traveling Waves in Nonlinear Magnetic Metamaterials

Agaoglou

Rothos

Frantzeskakis

et al. 2014

Int. J. Bifurcation Chaos

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In this work, we study a model of a one-dimensional magnetic metamaterial formed by a discrete array of nonlinear resonators. We focus on periodic and localized traveling waves of the model, in the presence of loss and an external drive. Employing a Melnikov analysis we study the existence and persistence of such traveling waves, and study their linear stability. We show that, under certain conditions, the presence of dissipation and/or driving may stabilize or destabilize the solutions. Our analytical results are found to be in good agreement with direct numerical computations.

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Section: Resultsmentioning

confidence: 99%

Bifurcation Results for Traveling Waves in Nonlinear Magnetic Metamaterials

Agaoglou

Rothos

Frantzeskakis

et al. 2014

Int. J. Bifurcation Chaos

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“…III) we use a value for the initial voltage equal to V 0 = 0.5 V (in physical units). For such a value of the voltage (similar, and even smaller, values have also been used in relevant experimental works [29][30][31][32][33][34]), it can be found that…”

Section: A the Nonlinear Lattice Modelmentioning

confidence: 91%

“…In the results below, we have fixed the parameters related to the soliton's amplitude as η = 1 and ε = 0.02, which correspond to an initial value of the voltage equal to V 0 = 0.5 V (similar, and even smaller, values have also been used in experiments [29][30][31][32][33][34]). Furthermore, we have fixed the initial soliton position to X 0 (0) = 1/2, and we have varied the frequency f and the soliton wave number K (recall that the latter sets the initial soliton momentum).…”

Section: A Analysis Of the "Regular" Srr-cpw Structurementioning

confidence: 99%

Quasidiscrete microwave solitons in a split-ring-resonator-based left-handed coplanar waveguide

Veldes

Cuevas²,

Kevrekidis

et al. 2011

Phys. Rev. E

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We study the propagation of quasidiscrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split-ring resonators. By considering the relevant transmission line analog, we derive a nonlinear lattice model which is studied analytically by means of a quasidiscrete approximation. We derive a nonlinear Schrödinger equation, and find that the system supports bright envelope soliton solutions in a relatively wide subinterval of the left-handed frequency band. We perform systematic numerical simulations, in the framework of the nonlinear lattice model, to study the propagation properties of the quasidiscrete microwave solitons. Our numerical findings are in good agreement with the analytical predictions, and suggest that the predicted structures are quite robust and may be observed in experiments.

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“…Applying Kirchhoff's laws to this system leads to the following set of differential equations governing wave propagation in the network C    . For this purpose, restricting moreover our study to weak amplitude and slow temporal variations of the wave envelope, we look for a solution of Equation (6) in the form…”

Section: The Dcgl Equation Withmentioning

confidence: 99%

“…The ability of solitons to propagate with small dispersion can be used as an effective means to transmit data, modulated as short pulses over long distances; one example of this is the ultra wideband impulse radio that has recently gained popularity [5]. More recently, the experimental, analytical and numerical study of a lefthanded nonlinear electrical lattice have been performed by English et al [6]. They found that the above system clearly supports backward wave propagation of plane waves, but also envelope solitons of the bright and dark type.…”

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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Backward-wave propagation and discrete solitons in a left-handed electrical lattice

Cited by 60 publications

References 32 publications

Bifurcation Results for Traveling Waves in Nonlinear Magnetic Metamaterials

Bifurcation Results for Traveling Waves in Nonlinear Magnetic Metamaterials

Quasidiscrete microwave solitons in a split-ring-resonator-based left-handed coplanar waveguide

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

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