Solitary Waves, Shock Waves and Singular Solitons of Gardner’s Equation for Shallow Water Dynamics

摘要

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.