Chaotic behavior, bifurcations, sensitivity analysis, and novel optical soliton solutions to the Hamiltonian amplitude equation in optical physics

Abstract

Abstract This study, highlights the exact optical soliton solutions in the context of optical physics, centering on the intricate Hamiltonian amplitude equation with bifurcation and sensitivity analysis. This equation is pivotal in optics which underpins the understanding of optical manifestations, encompassing solitons, nonlinear consequences, and wave interactions. Applying an analytical expansion approach, we extract diverse optical solutions, having trigonometric, hyperbolic, and rational functions. Next, we utilize concepts from the principle of planar dynamical systems to investigate the bifurcation processes and chaotic behaviors present in this derived system. Additionally, we use the Runge–Kutta scheme to carry out a thorough sensitivity analysis of the dynamical system. It has been verified through this analytical process that small variations in beginning conditions have negligible effects on the stability of the solution using bifurcation analysis. Validation via Mathematica software ensures the accuracy of these findings. Furthermore, we employ dynamic visualizations, such as 2D, 3D, and contour plots, to illustrate various soliton patterns, including kink, multi-kink, single periodic, multi-periodic, singular, and semi-bell-shaped configurations. These visual representations provide a glimpse into the fascinating behavior of optical phenomena. The solutions obtained via this proposed method showcase its efficacy, dependability, and simplicity in comparison to various alternative approaches.