ANALYTICAL SOLITON SOLUTIONS OF THE FRACTIONAL PERTURBED GERDJIKOV-IVANOV EQUATION USING THE JACOBI ELLIPTIC FUNCTION EXPANSION METHOD

Abstract

The perturbed Gerdjikov-Ivanov equation is important and has several applications in photonic crystal fibers and fiber optics. In this work, the Jacobi elliptic function expansion approach has been used to solve the Gerdjikov-Ivanov equation. The Jacobi elliptic function expansion method is used to find the solutions for solitary waves and soliton waves. We develop hyperbolic and trigonometric functions for solitary wave solutions and other types of soliton solutions, including dark and bright. The physical behaviors of the solutions can be illustrated in 2-D and 3-D using contours. Simulations are utilized to confirm the exact soliton solutions. With a few closing thoughts, we concluded the investigation.