Asymptotic shallow water equations: Modeling and solutions

In this paper we investigate an asymptotic limit for Green–Naghdi equation in the KdV scale with uneven bottom and considering the influence of two factors, surface tension and Coriolis effect. We establish the KdV equation of the new model by using Whitham technique then we find the analytic solution in case of flat bottom and Hs explicit consistent solution with correctors of order μ2 in case of uneven bottom. As well as, we obtain an Hs consistent solution for the asymptotic Green–Naghdi equation. Finally, we use Python to ensure the theoretical results through numerical simulations that admit to represent and validate the solution.