New Optical Solutions of the Fractional Gerdjikov-Ivanov Equation With Conformable Derivative

• Main Authors: Behzad Ghanbari, Dumitru Baleanu
• Format: Article
• Language: English
• Published: Frontiers Media S.A. 2020-05-01
• Series: Frontiers in Physics
• Subjects: PDEs; generalized exponential rational function method; non-linear Schrödinger equation; exact solutions; the perturbed Gerdjikov-Ivanov equation
• Online Access: https://www.frontiersin.org/article/10.3389/fphy.2020.00167/full

Finding exact analytic solutions to the partial equations is one of the most challenging problems in mathematical physics. Generally speaking, the exact solution to many categories of such equations can not be found. 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 in non-linear fiber optics. It also has many important applications in 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. 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 non-linear PDEs.