New diverse variety analytical optical soliton solutions for two various models that are emerged from the perturbed nonlinear Schrödinger equation

In this work we will extract new private types of impressive soliton solutions for two distinct models that describe propagation of waves in nonlinear optics. The first one is the perturbed Gerdjikov-Ivanov equation (PGIE) which act for the dynamics of solitons propagation that carry quantic nonlinearity of Schrödinger's equation while Schrödinger's equation is classically explored with cubic nonlinearity. In fact, it describes the solitons that carry quartic nonlinearity of Schrödinger's equation, specially the propagations of electromagnetic waves in nonlinear optical fibers. The second one is the perturbed nonlinear Schrödinger equation with Kerr-Law nonlinearity (PNSEWKL) that describes the behavior of wave propagation in nonlinear optical fibers. The study of these two models will contribute to high quality to long-distance communications, hence improve the telecommunications processes. The soliton solutions will be implemented to these two models for the first time in the framework of the Paul-Painleve approach method (PPAM). Furthermore, we will hold a comparison between our achieved results with that achieved previously by other authors.