Unravelling quiescent optical solitons: An exploration of the complex Ginzburg-Landau equation with nonlinear chromatic dispersion and self-phase modulation

In this investigation, we delve into the recovery of quiescent optical solitons amidst the onset of nonlinear chromatic dispersion (CD), employing the complex Ginzburg-Landau equation. Quiescent optical solitons, self-sustaining, locally distributed wave packets, uphold their shape and amplitude over extensive distances through a delicate equilibrium of nonlinearity and dispersion. Our scrutiny extends to four distinct forms of self-phase modulation structures, wherein we adopt the ( 1 & vartheta; ( zeta ) , & vartheta; ' ( zeta ) & vartheta; ( zeta ) ) \left(\frac{1}{{\vartheta }\left(\zeta )},\frac{{{\vartheta }}<^>{<^>{\prime} }\left(\zeta )}{{\vartheta }\left(\zeta )}) method, yielding solutions in hyperbolic function forms. This research meticulously examines the specific parametric constraints influencing the soliton presence, enhancing comprehension of the erratic behaviour by nonlinear waves and dynamic systems. Through vivid graphical representations, we provide insights into solution variations and their characteristics. These findings warn electronics and telecommunication engineers that nonlinear CD could halt global internet connectivity by preventing soliton transmission across borders. Hence, the imperative lies in preserving linear CD during transmission to avert such dire consequences. Furthermore, our study propels future research prospects, as we intend to substitute nonlinear CD with nonlinear cubic-quartic dispersive terms, expecting further discoveries to disseminate subsequently.