Dark and singular soliton solutions of perturbed Gerdjikov-Ivanov equation via the first integral method

Salam Subhaschandra Singh

doi:10.14419/ijpr.v6i2.13829

Abstract

This paper employs the first integral method in obtaining dark and singular soliton solutions of perturbed Gerdjikov-Ivanov equation showing that the method is a powerful tool for finding exact solutions of many nonlinear evolution (NLE) equations which are found in the studies of social dynamics, nonlinear science and engineering.Â Â

Highlights

This paper employs the first integral method in obtaining dark and singular soliton solutions of perturbed Gerdjikov-Ivanov equation showing that the method is a powerful tool for finding exact solutions of many nonlinear evolution (NLE) equations which are found in the studies of social dynamics, nonlinear science and engineering
The well-known nonlinear Schrodinger (NLS) equation is one of the most important nonlinear evolution (NLE) equations encountered in the studies of many branches of physics like quantum field theory (QFT) and fiber optics
The present paper studies the dark and the singular soliton solutions of a perturbed Gerdjikov-Ivanov (GI ) equation in (1 + 1) dimension

Summary

Introduction

The well-known nonlinear Schrodinger (NLS) equation is one of the most important nonlinear evolution (NLE) equations encountered in the studies of many branches of physics like quantum field theory (QFT) and fiber optics. Many extended versions of this equation with higher order nonlinearities have been extensively studied in many areas of nonlinear physics and mathematics. Mention may be made of higher order nonlinear Schrodinger (HONLS) equation and derivative nonlinear Schrodinger (DNLS) equation. The GI equation describes optical soliton propagation in (1+1)dimensions. This equation has been studied by many authors in recent years. 2. Reduction of a given nonlinear partial differential equation to a nonlinear ordinary differential equation. Let us describe how a given nonlinear partial differential equation (NLPDE) can be reduced to a nonlinear ordinary differential equation (NLODE). In terms of the new function U(ξ) and its derivatives, Eq (2) is transformed into another polynomial equation of the form. We are to solve this reduced nonlinear ordinary differential equation (RNLODE)

Algorithm of the first integral method

Reduction of perturbed gerdjikov-ivanov equation to a NLODE

Conclusion