Abstract
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.
Solitary waves and modulation instability with the influence of fractional derivative order in nonlinear left-handed transmission line
