<p>In this study, the classical Benney-Luke equation has been expanded by adding a coefficient to the term representing diffusion, thus making the model more suitable for physical realities. This modification aims to provide a deeper understanding of fluid behavior by uncovering the mysteries hidden within the model's coefficients. With the extended equation, it is possible to model complex wave behavior in fluid systems such as shallow water wave dynamics more flexibly and accurately. The traveling wave solutions are obtained by analytical expansion method and compared with existing solutions in the literature and certain constraint conditions are taken into account to ensure the physical validity of the solutions. It is observed that the obtained solutions exhibit a stable structure with constant profile and amplitude, soliton-like behavior and consistent propagation in infinite space–time. In addition, the effects of diffusion on the wave dynamics are studied in detail and the stability of the solution is evaluated by mathematical analysis. When the solutions are compared with the existing results in the literature, it is seen that the proposed model offers a wider parameter space and allows a more realistic representation of physical phenomena. In this respect, the study makes significant contributions in terms of both theoretical depth and physical meaning by surpassing the previous approaches in the literature and paves the way for more accurate modeling of fluid systems.</p>