一类变系数KP方程的Painleve分析和容许变换

讨论一类来自于表面波传播的变系数ＫＰ方程的完全可积性．证明了此类方程通过容许变换化为常系数ＫＰ方程或Ｋｄｖ方程时系数所应满足的条件，此条件即为此类方程完全可积的充分必要条件．

Painleve analysis and allowed transformations of a class of varieble coefficient KP equations

This paper discusses the complete integrability of a class of generalized KP equation with space and time dependent coefficients, which is known to have a physical application in the propagation of surface waves in straits with varying depth and width. It is shown that the constraints which the variable coefficient functions must satisfy for the considered KP equation to pass the Painleve tests for complete integralility are the same in order that the equation may be transformed into either the KP equation or the Kdv equation. These provide necessary and sufficient conditions for the KP equation to be complete integrable.