A study of shallow water waves with Gardner's equation

In this paper the dynamics of solitary waves governed by Gardner's equation for shallow water waves is studied. The mapping method is employed to carry out the integration of the equation. Subsequently, the perturbed Gardner equation is studied, and the fixed point of the soliton width is obtained. This fixed point is then classified. The integration of the perturbed Gardner equation is also carried out with the aid of He's semi-inverse variational principle. Finally, Gardner's equation with full nonlinearity is solved with the aid of the solitary wave ansatz method.