Abstract
We analyze the particular behavior exhibited by a chaotic waves field containing Peregrine soliton and Akhmediev breathers. This behavior can be assimilated to a tree with “roots of propagation” which propagate randomly. Besides, this strange phenomenon can be called “tree structures”. So, we present the collapse of dark and bright solitons in order to build up the above mentioned chaotic waves field. The investigation is done in a particular nonlinear transmission line called chameleon nonlinear transmission line. Thus, we show that this line acts as a bandpass filter at low frequencies and the impact of distance, frequency and dimensionless capacitor are also presented. In addition, the chameleon’s behavior is due to the fact that without modifying the appearance structure, it can present alternatively purely right- or left-handed transmission line. This line is different to the composite one.
Highlights
Metamaterials are materials which have both the permeability ( μ ) and the permittivity ( ε ) parameters are set negative at the same frequency [1] [2]
We have studied an electromagnetic wave propagation when second-order dispersion and cubic-nonlinearity effects come into play. Those effects interact in a modulable electrical transmission line in order to build up dark or bright soliton
Collective coordinates technique of investigation has been used in order to study internal and external behaviors of electromagnetic light pulse
Summary
Metamaterials are materials which have both the permeability ( μ ) and the permittivity ( ε ) parameters are set negative at the same frequency [1] [2]. There exists a strange phenomenon directly related to the investigation of extreme events It appears when a chaotic waves field is generated by modulation instability. It has been shown that Raman effect can induce the appearance of particular “tree structure” with roots which can be called “roots of propagation” [24] [27] Authors else such as Dudley [28], sustains that such “tree structures” correspond to signatures of analytic nonlinear Schrödinger equation solutions in chaotic modulation instability [24]. In this paper, based on the work of Fukushima et al [29], Marquié et al [23] and that of Togueu et al [30], we model the electromagnetic wave behavior by a nonlinear Schrödinger equation This equation includes second-order dispersion and cubic-nonlinearity in a modulable transmission line. Applying Kirchhoff’s laws to the circuit model, we can obtain the following voltage propagation equations [30]:
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