A simple approach for reducing the order of equations with higher order nonlinearity

In this paper, we introduce a simple approach to reduce the order of equations with higher order nonlinearity. We choose the generalized forms of the KdV equation, the Camassa–Holm equation and the Zakharov–Kuznetsov equation to illustrate the validity and advantages of the approach. Then the explicit solutions with different physical structures of the reduced equations can be discussed further. The approach used here can be applied to some other nonlinear equations with higher order nonlinearity and is also suitable for some higher dimensional models.