中文摘要：

利用不变子空间方法研究一般的三阶非线性微分算子的分类问题.证明了当三阶算子容许次于最大维（六维）不变子空间时,它可以被表示为各参量的平方形式,得到了常系数三阶非线性微分算子在六维子空间的完全分类.最后通过一些例子演示利用不变子空间方法约化方程及求精确解的过程.

英文摘要：

The paper discusses the general third-order nonlinear dillerentlal operators by means of the invariant subspace method. It is shown that they are quadratic forms while preserving invariant subspace of submaximal dimension. A full description of the third-order quadratic operators with constant coefficients which preserve six-dimensional invariant subspaces are obtained. Some examples are given to illustrate the reduction and construction of special solutions of the resulting evolution equations with quadratic nonlinearities.