变系数Zakharov－Kuznetsov方程的容许变换和Painlev分析

Allowed Transfor mations and Paionleve Property of the Variable-Coefficient Zakharov-Kuznetsov Equations

讨论了来自于磁化的等离子体中非线性离子声波传播的Ｚａｋｈａｒｏｖ－Ｋｕｚｎｅｔｓｏｖ（ＺＫ）方程及变系数ＺＫ方程。得到了ＺＫ方程的奇性流形方程的通解；证明了变系数ＺＫ方程能够通过容许变换化为ＺＫ方程的系数所应满足的条件并不等价于它具条件ｐａｉｎｌｅｖ性质时的系数所应满足的条件。

T he zak harov-K uznetsov(ZK)equation and its variable-coefflcient generalization whichgoverns monlinear ion-acoustic waves in a magnetized plasma is considered.The general solution ofthe singular manifold equation of the ZK equation is obtained.It is shown that the constraints whichthe variable coefficlent functions for the equation to possess the conditional Painleve property are notequivalent those in order that the equation may be transformed into the constant coefficient equation.