Reduction of the Sharma–Tasso–Olver equation and series solutions

This paper considers series solutions of the Sharma–Tasso–Olver (STO) equation. By using the extended homogenous balance method, we reduce the STO equation to a linear PDE and obtain Bäcklund transformation of it. Furthermore, the self-transformation of solutions for the STO equation is obtained. By the Bäcklund transformation and various series solutions of the PDE, abundant exact solutions of the STO equation are obtained including the multi-solitary wave solution, trigonometric function series solution, rational series solution and solution consisting of the three types of solutions.