This paper unearths solitary wave in a simplified electrical model practical of the nonlinear left-handed transmission electrical line having series capacitance and shunt inductance. The detailed study of the practical model digs out that by taken a good parameter of the lattice, the obtained equation from the evolution of the wave envelope can be reduced to a one-dimensional fractional nonlinear Schrödinger equation, which gives the pipe of the dark solitons propagation. By simulating transient circuits, the evolution of the soliton and modulational instability gain were demonstrated in the areas of perturbation frequency, pulsation, nonlinearity and signal strength with a continuous wave type input signal. It has also been shown that increased perturbation, nonlinearity and signal strength in simplified metamaterial models of short nonlinear transmission lines lead to the formation of Schrödinger dark solitons and increased instability gain in a continuous pulse structure. The establishment of Schrödinger solitons and the progressive distance of a point, i.e. the fractional parameter α = 1, could reduce the width of the signal bandwidth and the breaking of the symmetry of the instability gain in the simplified electrical model practical of the nonlinear left-handed transmission electrical line, so that the evolution of the system cannot be controlled due to the memory effect, which can find important practical applications in communication systems.
The resolution of the reduced fractional nonlinear Schrödinger equation obtained from the model describing the wave propagation in the left-handed nonlinear transmission line presented by Djidere et al recently, allowed us in this work through the Adomian decomposition method (ADM) to highlight the behavior and to study the propagation process of the dark and bright soliton solutions with the effect of the fractional derivative order as well as the Modulation Instability gain spectrum (MI) in the LHNLTL. By inserting fractional derivatives
The resolution of the reduced fractional nonlinear Schrodinger equation obtained
from the model describing the wave propagation in the left-handed nonlinear
transmission line presented by Djidere et al recently, allowed us in this work
through the Adomian decomposition method (ADM) to highlight the behavior
and to study the propagation process of the dark and bright soliton solutions
with the e ect of the fractional derivative order as well as the Modulation Instability
gain spectrum (MI) in the LHNLTL. By inserting fractional derivatives
in the sense of Caputo, we used ADM to structure the approximate solitons
solutions of the fractional nonlinear Schrodinger equation reduced with fractional
derivatives. The pipe is obtained from the bright and dark soliton by
the fractional derivatives order (see Figures 2 and 5). By the bias of MI gain
spectrum the instability zones occur when the value of the fractional derivative
order tends to 1. Furthermore, when the fractional derivative order takes small
values, stability zones appear. These results could bring new perspectives in
the study of solitary waves in left-handed metamaterials, as the memory e ect
could have a better future for the propagation of modulated waves because we
also show in this article that the stabilization of zones of the dark and bright
solitons could be described by a fractional nonlinear Schrodinger equation with
small values of fractional derivatives order. In addition, the obtained signi cant
results are new and could nd applications in many research areas such as in
the eld of information and communication technologies.
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