Abstract
The dynamics of two-layered shallow water waves is studied in this paper by the aid of coupled potential-Korteweg-de Vries (pKdV) equation. There are two types of models that are considered. The first model yields solitary waves as well as shock wave solutions. The second model yields shock wave solutions only. The ansatz method is applied to retrieve the solitary wave as well as the shock wave solutions of both models. In both cases the time-dependent coefficients of dispersion and nonlinearity are considered, in order to keep the model closer to reality. Numerical simulations demonstrate the presence of soliton behaviour that is both rich and diverse.