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

Zara Hassan,J F Gómez-Aguilar,Nauman Raza

doi:10.1007/s11082-021-03123-3

Abstract

The objective of this manuscript 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 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 them 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.

Highlights

In the field of information technology, the transmission mechanism is a crucial component
The objective of this research is to study the collective variable (CV) technique to explore an important form of Schrodinger equation known as the Gerdjikov-Ivanov (GI) equation which expresses the dynamics of solitons for optical fibers in terms of pulse parameters
We have investigated the optical solitons for both dimensionless as well as generalized perturbed GI equations by applying a CV approach

Summary

Introduction

In the field of information technology, the transmission mechanism is a crucial component. The significant adoption of optical fiber is in telecommunications [1,2,3,4,5]. This structure has been employed for high-performance and long-distance data transport due to its enhanced bandwidth capabilities. It is employed to relay signals from communication devices such as the telephone, television and internet between distant areas. Recent research has shown that using dispersion-managed solitons for data transfer will significantly increase the ability of fiber-optic links [2, 3]. Because of its extensive applications in nonlinear optics, solitons theory is gaining a lot of interest. A variety of analytical and numerical methods have been presented [4, 5]

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