<p>This study presents a comprehensive analysis of the nonlinear dynamics of the Gardner’s equation by combining analytical, dynamical and stability approaches within a unified framework. Exact traveling wave solutions are constructed using the Generalized Kudryashov-Auxiliary Jacobian Method (GKAJM), yielding a diverse class of structures including solitons, periodic waves and kink-type solutions. The governing equation is reduced to a planar dynamical system via a Galilean transformation, enabling a detailed investigation of equilibrium points, phase portraits and bifurcation behavior. Linear stability is examined through eigenvalue analysis, while chaotic dynamics are identified using standard indicators, demonstrating sensitivity to system parameters and initial conditions. In addition, Ulam-Hyers stability is established to assess the robustness of the obtained solutions. Graphical visualizations, including 2-dimensional, contour and 3-dimensional plots, are provided to illustrate the physical characteristics of the wave solutions. The results offer deeper insight into the interplay between nonlinear wave structures and dynamical properties and provide a systematic framework applicable to a broad class of nonlinear evolution equations.</p>