<p>In this study, we explore different methods to investigate the nonlinear Helmholtz equation. First, to investigate the dynamic behavior of the system, we apply bifurcation analysis, visually depicted via phase portraits. Next, we introduce the periodic functions into the dynamical system to explore chaotic, which introduces complexity into the system and leads the emergence of chaotic dynamics. We graphically present these dynamics with the aid of 3D, 2D phase plots and time plots. We then examine the chaotic nature of the system in detail, revealing intricate patterns of instability. By changing the initial conditions, we study the multistability, which demonstrates how the system shows different stable states by taking selected parameters. We perform the sensitivity analysis to evaluate how small changes in the system’s parameters affect its overall behavior and provide a deeper understanding of its robustness and responsiveness to perturbations. Finally, we apply the Sardar subequation method to derive exact solutions for the governed equation. These solutions are graphically represented through 3D plots with projections, polar plots, and 2D plots of the real, absolute, and imaginary components of the solutions. This study offers a thorough investigation of the equation by employing bifurcation analysis, chaotic dynamics, multistability, sensitivity analysis, and the Sardar subequation method to uncover the complex behaviors that arise in nonlinear wave propagation. The model’s strength lies in accommodating wide restoring spatial symmetry and beam angles, while its complexity poses a challenge. The proposed methods effectively uncover intricate wave phenomena, making them highly applicable to nonlinear wave propagation and optical systems. The novelty lies in the dynamic analysis of the nonlinear Helmholtz equation through bifurcation, chaos, multistability, and sensitivity studies.</p>