Optical soliton perturbation with quadratic-cubic nonlinearity / Mir Asma - Mir, Asma (2020)
Solitons can be defined as wave packets that can travel undistorted across long distances even transcontinental and transoceanic. They serve as modern telecommunication means through cables and optical fibers for fast Internet activities. To maintain high-fidelity and time sensitive transmission, optical pulses manage the efficient flow of data. From the last few years, Nonlinear Schrödinger Equation (NLSE) has been a great attraction of research activities across the globe. The governing model is the Nonlinear Schrödinger Equation (NLSE). From a mathematical standpoint, NLSE is a nonlinear partial differential equation (PDE) that has been studied in a variety of other areas of Physics and Mathematics. Solitons maintain subtle harmony that persists between nonlinear and dispersive effects. In order to support this theoretical concept, it is possible to simulate some nonlinearities in NLSE that depend on the light refractive index and the nature of the fiberglass. These nonlinearities are quadratic, cubic (kerr), quintic, quadratic-cubic, cubic-quintic, polynomial, logarithmic and saturable. Recently, a some new forms of nonlinear refractive index have been proposed and studied. These include anti-cubic, generalized anti-cubic and non-local types. At a most recent time, a new model is now proposed, at least analytically, with experimental evidence pending. This is Kudryashov’s equation. In the present study, quadratic-cubic (QC) nonlinearity is the focus, including the effects of perturbation terms of similar functional dependence. A wide variety of analytical methods are implemented to the perturbed NLSE to gain a complete understanding of the pulse dynamics, both analytically as well as numerically. These perturbation terms are mostly of Hamiltonian type that permits integrability of the perturbed NLSE. The spectrum of soliton solutions, that emerge from these algorithms are of bright, dark singular and combo solitons, which depends on the sign of discriminant and these findings are illustrated numerically too. The method of undetermined coefficients fortifies a particular solution of nonhomogeneous NLSE in the form of bright, dark, singular and W-shaped solitons. Semi-inverse variational principle (SVP) is used to secure bright solitons that are expressed as Gauss’ hypergeometric functions. SVP fails to retrieve dark and singular soliton solutions because of the divergence of the corresponding stationary integrals. Adomian decomposition method (ADM) cooperated to recover bright, dark, and W-shaped solitons numerically. The numerical schemes are further consolidated with the help of error plots. The collective variables (CV) approach yielded parameter dynamics of the perturbed solitons. The CV is an approach for integrating the residual field of optical Gaussons, which helps to figure out the types of soliton solutions. This study is an addendum to the previously reported results on optical solitons solely, in view of the fact that, its fundamental nature as well as its potential applications to optoelectronic communication. Analytical results open up a new horizon of experiments with optical solitons to facilitate a soliton based optical communication system.