In this article, we investigate a generalized perturbed-KdV equation, which describes the physical mechanism of sound propagation in fluid and appears in the applications of aerodynamics, acoustics, and medical engineering. The improved \((G'/G)\) -expansion method is employed to explore the hyperbolic and trigonometric solutions of the equation. Compared to traditional methods, we provide the condition that parameter \(\xi \) is not subject to any restrictions. Additionally, the polynomial function method is utilized to look for the lump solution of the generalized perturbed-KdV equation based on the Hirota’s bilinear form. From the results, it can be seen that this method is very simple and effective, with few constraints on unknown parameters. Finally, graphical representations such as 3-dimensional, contour, and density plots are shown with the help of the Mathematica software.
