Painlevé Property and Allowed Transformations of the Variable-Coefficient Zakharov-Kuznetsov Equation

In this letter, we discuss the Painlevé property and allowed transformation for the variablecoefficient Zakharov-Kuznetsov equation which governs nonlinear ion-acoustic wqves in a magnetized plasma. The general solution of the singular manifold equation and stability solution of the VCZK equation are obtained. To prove some information of the integrability of the ZK equation, we prove the constraints that the variable-coefficient functions for the equation to possess the Painlevé property are not equivalent in order that the equations may be transformed into the constant coefficient equation. So we confirm that the ZK equation is not integrable.