Novel optical solitons to the perturbed Gerdjikov–Ivanov equation via collective variables

Abstract

The objective of this research is to study the collective variable (CV) technique to explore an important form of Schrödinger equation known as the Gerdjikov-Ivanov (GI) equation which expresses the dynamics of solitons for optical fibers in terms of pulse parameters. These parameters are temporal position, amplitude, width, chirp, phase, and frequency known as collective variables (CVs). This is an effective and dynamic mathematical gadget to obtain soliton solutions of non-dimensional as well as perturbed GI equations. Moreover, an established numerical scheme that is the fourth-order Runge-Kutta method is exerted for the numerical simulation of the revealing coupled system of six ordinary differential equations which represent all the CVs included in the pulse ansatz. The CV approach is used to determine the evolution of pulse parameters with the propagation distance and illustrated it illustrated it graphically. Furthermore, Figures show the compelling periodic oscillations of pulse chirp, width, frequency and amplitude of soliton. For various values of super-Gaussian pulse parameters, the numerical behavior of solitons to illustrate variations in CVs is provided. Other significant aspects with regards to the current investigation are also inferred.

On the optical soliton solutions to the fractional complex structured (1+1)-dimensional perturbed gerdjikov-ivanov equation

“…Besides these, there are some actual articles given fractional calculus about FPGIE, such as M-fractional PGIE [33], Riemann-Liouville FPGI model [34], and FPGIE in conformable sense [35]. In addition, conservation laws for PGIE with Lie symmetries [36], abundant wave solutions [37], novel optical solitons [38], fractional form [39]. Computational extracting solutions [40].…”

Investigation of optical soliton solutions for the perturbed Gerdjikov-Ivanov equation with full-nonlinearity

“…Besides all, there are some actual papers in view of fractional calculus about pGI equation such as M-fractional pGI equation [51] , fractional pGI in conformable sense [52] and Riemann-Liouville fractional pGI model [53] . In addition, conservation laws for pGI with Lie symmetries [54] , abundant wave solutions [55] , new solitary wave solutions [56] , fractional form [57] , novel optical solitons [58] and computational extracting solutions [59] .…”