This study investigates bifurcation, chaos, and stability analysis for the second fractional WBBM model, a significant model in shallow water wave research. The dynamic system is derived using the Galilean transformation. Planar dynamic system techniques are employed to analyze bifurcations, chaos, and sensitivities. The results reveal diverse behaviors, including quasi-periodic, periodic, and chaotic motion. Various soliton structures, such as bright and dark solitons, kink and anti-kink waves, are explored through visual illustrations. The study highlights the importance of chaos analysis in understanding complex system dynamics, prediction, and stability. The methods used are efficient, concise, and effective, enhancing understanding of the model and suggesting broader applications for nonlinear systems. The study also improves understanding of shallow water nonlinear dynamics, including waveform features, bifurcation analysis, sensitivity, and stability. Insights into dynamic properties and wave patterns are revealed. The second fractional 3D WBBM model is analyzed using conformable derivatives and the Galilean transformation. Bifurcation analysis reveals different equilibrium points and their stability. Chaotic behaviors are observed under varying disturbance intensities and frequencies. Sensitivity analysis shows how initial conditions affect the system's behavior. Soliton waveforms, including bright and dark solitons, kink and anti-kink waves, are analyzed. The study provides novel insights into the dynamics and behavior of the model, emphasizing the significance of interdisciplinary approaches in addressing complex challenges in modern research.This study investigates bifurcation, chaos, and stability analysis for the second fractional WBBM model, a significant model in shallow water wave research. The dynamic system is derived using the Galilean transformation. Planar dynamic system techniques are employed to analyze bifurcations, chaos, and sensitivities. The results reveal diverse behaviors, including quasi-periodic, periodic, and chaotic motion. Various soliton structures, such as bright and dark solitons, kink and anti-kink waves, are explored through visual illustrations. The study highlights the importance of chaos analysis in understanding complex system dynamics, prediction, and stability. The methods used are efficient, concise, and effective, enhancing understanding of the model and suggesting broader applications for nonlinear systems. The study also improves understanding of shallow water nonlinear dynamics, including waveform features, bifurcation analysis, sensitivity, and stability. Insights into dynamic properties and wave patterns are revealed. The second fractional 3D WBBM model is analyzed using conformable derivatives and the Galilean transformation. Bifurcation analysis reveals different equilibrium points and their stability. Chaotic behaviors are observed under varying disturbance intensities and frequencies. Sensitivity analysis shows how initial conditions affect the system's behavior. Soliton waveforms, including bright and dark solitons, kink and anti-kink waves, are analyzed. The study provides novel insights into the dynamics and behavior of the model, emphasizing the significance of interdisciplinary approaches in addressing complex challenges in modern research.