Abstract
The paper addresses the dynamics of shallow water waves that are governed by the Gardner equation, that is a generalized version of the well-known Korteweg-de Vries equation. Exact solutions are obtained in presence of shoaling and advection terms with power law nonlinearity. The paper integrates the equation by the aid of G'/G-expansion method. This approach reveals singular soliton as well as shock wave solutions to the model. The solution existence criteria, also known as constraint conditions, are also displayed.