In this article, the perturbed Gerdjikov-Ivanov equation, describing the dynamics of propagation of solitons, is studied. The balanced modified extended tanh-function and the non-balanced Riccati-Bernoulli Sub-ODE methods are used for the first time to obtain the new optical solitons of this equation. The obtained results give an accurate interpretation of the propagation of solitons. We performed a comparison between our results and those in the literature. The efficiency of these methods for constructing the exact solutions has been demonstrated. It is shown that these different techniques reduce the large number of calculations.