Abstract
In this paper, we have studied a generalized scale-invariant analog of the well-known Korteweg-de Vries (KdV) equation. The generalized scale-invariant analog of the Korteweg-de Vries (SIdV) plays as a bridge between the KdV equation. The generalized SIdV model was discovered recently, and shares the same one-soliton solution as the KdV equation. By employing four mathematical methods, several types of exact and solitary wave solutions are established. For the physical behavior of the model, some solutions are plotted graphically by imparting specific values to the parameters under constrain condition. Hence, reconnoitered elucidations have profitable rewards in the field of mathematical physics.