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.