On the structure of unsteady korteweg-de vries model arising in shallow water

In this article, the modified Kudryashov approach and (1G′)-expansion approach are utilized to extract some new analytical solutions to the unsteady Korteweg-de Vries equation. In nonlinear sciences, this equation is very important. As a result, a variety of new exact solutions are acquired for the aforementioned nonlinear model. Moreover, the two dimensional, three dimensional, and contour shapes are visualized with the aid of latest scientific tools. We found four forms of explicit solutions such as the hyperbolic, trigonometric, exponential, and rational function solutions. It has been demonstrated that the proposed techniques are highly efficient and practical for the aforementioned issues, as well as additional NLEEs that appear in engineering domains and mathematical physics.