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.

中文翻译：

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Drinfel'd–Sokolov–Wilson方程的一致Riccati展开和有理解

一致的Riccati展开（CRE）用于Drinfel'd–Sokolov–Wilson（DSW）方程。它证明了DSW方程是CRE可解系统。DSW方程的双线性形式是通过截断的Painlevé方法构造的。通过选择DSW方程的双线性形式的二次函数，可以明确找到一个包含暗和亮类型的流氓波。有理解与其他复杂波之间的相互作用是通过将多项式函数与任意函数混合而生成的。通过选择适当的参数以图形方式分析这些类型的有理解。