Abstract
We consider a second order wave equation of KdV type that was recently proposed as an improved approximation of shallow water wave propagation compared with the KdV equation. We have solved this nonlinear wave equation by using the auxiliary equation method. A class of soliton-like solutions obtained, for the first time. Parametric conditions for the existence and uniqueness of these exact solutions are presented. The solutions comprise novel solitary wave as well as the shock wave solutions, illustrating the potentially rich set of soliton solutions of the newly proposed KdV model. These exact solutions will be useful to explain some physical phenomena found in the nonlinear water waves.