Closed form solutions of Gerdjikov–Ivanov equation in nonlinear fiber optics involving the beta derivatives

Abstract

In this paper, the closed form solutions of Gerdjikov–Ivanov equation with the beta derivatives are studied. This equation has quintic nonlinearity coefficients and group velocity dispersion, which shows the pulse behaviors in nonlinear fiber optics. It also has lots of significant applications in photonic crystal fibers. To this end, abundant families of closed form solutions in single or combined forms such as bright, singular, dark-singular are obtained by two systematic methods. Moreover, chaotic solutions are emerge as well. In order to understand dynamic behaviors of the begotten results, some computer simulations of the solutions are presented via some graphs with different values of the parameter beta. The results show that the approaches in this paper are efficient and direct methods to solve various fractional differential equations in mathematical physics.