<p>This study presents a novel framework for investigating soliton solutions to the generalized reaction Duffing equation, a key model in science and engineering that describes damped oscillators with complex potentials, capturing intricate behaviors. Its applications span electrical engineering, biomechanics, climate studies, earthquake research, and chaos theory, driven by its rich nonlinear dynamics. Using the Sardar Sub Equation and New Sub Equation methods, the study reveals a variety of exact traveling wave solutions, including hyperbolic, Jacobi, and trigonometric forms such as bell-shaped, kink, anti-kink, and periodic waves, offering deep insights into wave dynamics. Qualitative analysis is conducted through sensitivity analysis, bifurcation analysis, and chaos analysis. Sensitivity analysis examines the system’s behavior under varying initial conditions and parameter changes, while bifurcation analysis explores structural shifts in dynamics. Additionally, chaos analysis provides a comprehensive understanding of chaotic and periodic behaviors. This analysis is vital for grasping system dynamics, the influence of minor perturbations, and transitions between stable and chaotic states. Our work is further compared with existing studies, demonstrating its novelty and uniqueness</p>