Consistent Riccati expansion and rational solutions of the Drinfel’d–Sokolov–Wilson equation

The consistent Riccati expansion (CRE) is used to the Drinfel’d–Sokolov–Wilson (DSW) equation. It demonstrates that the DSW equation is the CRE solvability system. The bilinear form of the DSW equation is constructed by the truncated Painlevé method. One rogue wave including the dark and bright types is explicitly found via choosing a quadratic function in the bilinear form of the DSW equation. The interactions between rational solutions and other complicated waves are generated by mixing the polynomial function with an arbitrary function. These types of rational solutions are analyzed graphically by selecting appropriate parameters.