基于微分特征集理论和算法, 提出在一定条件下判定偏微分方程(组)非古典对称存在性的机械化方法.该方法对Clarkson P A提出的关于偏微分方程(组)的非古典对称的公开问题给出了部分回答,为完全解决该问题提供了一个思路.通过若干个发展方程的非古典对称的确定说明了该方法的有效性.

Based on the differential characteristic set theory and algorithm, a mechanical method is proposed to determine the existence of nonclassical symmetry of partial differential equations. By using the method, we get the partial answer for an open problem proposed by Clarkson P A on nonclassical symmetry of partial differential equations and a potential way to completely solve the problem. To illustrate the effectiveness of our method, the nonclassical symmetries of several evolution equations are determined by using the proposed method.