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.