Analyzing optical solitary waves in Fokas system equation insight mono-mode optical fibres with generalized dynamical evaluation.

This study focuses on the Fokas system equation, which explains the nonlinear pulse propagation in single-mode fibres. The proposed new sub-equation approach and the modified Khater's method extract a more efficient and broad range of soliton solutions. These include multiple anti-kink, anti-kink, flat anti-kink, combined bright-periodic, multiple bright, v-shaped, bell-shaped, and flat bell-shaped singular soliton. The primary innovation of this paper lies in its discovery of a set of novel soliton solutions that provide insight into the interaction mechanisms of nonlinear waves within the realm of nonlinear physics. The travelling wave patterns of the model are graphically presented with suitable parameter values using the modern software Mathematica. The visual representation of the solutions in 3D, 2D, and contour surfaces enhances understanding of parameter impact. We conducted a sensitivity analysis on a newly developed dynamic framed structure that controls pulses using the velocity factor of the soliton wave. The proposed model's dynamics were observed and presented as bifurcation analysis, quasi-periodic chaotic, periodic systems and quasi-periodic. We anticipate that our research findings will catalyze advancing the study of nonlinear theory and its applications in optical fibres. This analysis confirms the effectiveness and reliability of the method employed, demonstrating its applicability in discovering travelling wave solitons for a wide range of nonlinear evolution equations. [ABSTRACT FROM AUTHOR]