Instability modulation and novel optical soliton solutions to the Gerdjikov-Ivanov equation with M-fractional

Abstract

The modified exponential function method is used to obtain some new analytical solutions of the nonlinear Gerdjikov-Ivanov equation with the M-fractional operator. The novel obtained solutions are expressed in hyperbolic, trigonometric, and exponential function forms. Moreover, the instability modulation and gain spectra of the Gerdjikov-Ivanov equation are also analyzed. Constraints conditions are utilized to verify the existence of the solutions. Presented solutions are novel, satisfy and verify the M-fractional Gerdjikov-Ivanov equation.