Abstract
In this research, the model under consideration is the Fokas system that simulates the dynamics of wave through single mode fiber optics. Dark, bright, kink and periodic optical solitons are yielded using Painlevé approach and semi-inverse variational principle. The constraint conditions for the existence of the solutions also merge during the derivation. The obtained solutions are discussed to depict and support theoretical outcomes through the phase portraits. Further, we have applied the idea of bifurcation and chaos theories to get a better understanding of the planar dynamical system obtained from the studied system. The chaotic solutions for the perturbed dynamical system are also obtained and displayed through graphs. The sensitivity analysis of the model is also investigated, and the results show that the given model is not highly sensitive and is stable. These unique ideas employ symbolic computations to provide dynamical as well as potent mathematical tool related to tackling diverse benign nonlinear wave problems. The dynamics analysis method and numerical results are meaningful and helpful to further study on the reliability control of Fokas system.