Abstract
In this article, the Fokas-system represents the nonlinear pulse propagation in monomode optical fibers. Soliton solutions of the Fokas-system has been determined using three algorithmic schemes including singular manifold method, the -expansion method and Sine-Gordon expansion. The proposed methods have been applied to extract various types of solutions such as bright, dark, singular, periodic and complexitons. Moreover, the constraint conditions for the existence of the solutions will be discussed. To grasp the debated approaches, the obtained solutions are discussed with 3D surface plots and 2D line plots to visualize and support the theoretical results. The extracted results indicate that the proposed methods are excellently explore nonlinear evolution equations. The presented paper provides full spectrum of solutions for the Fokas-System. These novel approaches are used through the symbolic computations impart a dynamical and potent mathematical implement for solving various benevolent nonlinear wave problems. The resulting solutions are novel, intriguing, and potentially helpful for understanding energy transit and diffusion processes in mathematical models of several disciplines of interest, including nonlinear optics.