An improved CRE method and novel interaction solutions to a fifth-order nonlinear equation

The consistent Riccati expansion (CRE) method is powerful for deriving interaction solutions of nonlinear evolution equations. We improve the CRE method by extending the Riccati equation to the Riccati-Bernoulli equation. The improved CRE method solves nonlinear evolution equations by utilizing both the Riccati and Bernoulli equations. The effectiveness and convenience of the improved CRE method have been demonstrated by a new fifth-order equation. With this method, more types of interaction solutions can be constructed. These include not only soliton-cnoidal solutions but also exponential-elliptic and other interaction solutions. Moreover, the improved CRE method can be applied to construct interaction solutions of other nonlinear systems.