New Optical Solutions of the Fractional Gerdjikov-Ivanov Equation With Conformable Derivative
Behzad Ghanbari, Dumitru Bǎleanu
Abstract
Finding the exact solution of partial equations is one of the most challenging problems in mathematics. In most cases, there is no exact solution to this set of equations. In these cases, the use of numerical and approximate methods is inevitable. Nevertheless, the exact PDE solver methods are always preferred because they present the solution directly without any restrictions to use. This article aims to examine the perturbed Gerdjikov-Ivanov equation in an exact approach point of view. This equation plays a significant role, and has many important applications in nonlinear fiber optics and photonic crystal fibers. To this end, firstly, we obtain some novel optical solutions of the equation via a newly proposed analytical method called generalized exponential rational function method. In order to understand the dynamic behavior of these solutions, several graphs are plotted for some specific choices for the parameters. To the best of our knowledge, these two techniques have never been tested for the equation in the literature. The findings of this article may have a high significance application while handling the other nonlinear PDEs.