Optical solitons for the nonlinear perturbed Gerdjikov-Ivanov equation with constant and variable coefficients

The exact soliton solutions of perturbed Gerdjikov-Ivanov equation with both constant and variable coefficients are constructed in this work through the application of the modified F-expansion method. This method is used for the very first time on the considered equation. As a result, the traveling wave solutions including soliton solutions are obtained. These soliton solutions enhance understanding of nonlinear phenomena in the fields of photonic crystal fibers, fiber optics and nonlinear fiber optics. The explanation of the obtained results is provided by drawing some 2-dimensional and 3-dimensional graphs using Mathematica. Furthermore, this study discusses the modulation instability for the considered model. The considered method is found to be effective, simple and useful to study the perturbed Gerdjikov-Ivanov equation.