Solitary wave and shock wave solutions to a second order wave equation of Korteweg–de Vries type

This paper obtains the solitary wave as well as the shock wave solutions to the second order wave equation of Korteweg–de Vries type that was first proposed in 2002. The ansatz method is used to retrieve these solutions. The domain restrictions as well as the parameter regimes are all identified in the process of obtaining the solution.