确定线性偏微分方程组可积系统的对合特征集方法

ON COMPLETELY INTEGRABLE SYSTEM OF LINEAR PDES WITH INVOLUTIVE CHARACTERISTIC SET METHOD

基于Ritt-Wu特征集方法和Riquier-Janet理论,给出一种将线性微分方程组化成简单标准形式的有效算法．该算法通过消去冗余和添加可积条件获得线性微分方程组的完全可积系统(有形式幂级数解)或不相容判定．该算法不仅适用于常系数的线性偏微分方程组,而且对于变系数(以函数为系数)仍然有效．作者还给出了完全可积系统判定定理及其严格证明．

Based on the Ritt-Wu＇s characteristic set method and Riquier-Janet theory, an algorithm to reduce the linear PDE system to a normal form is presented. With this algorithm, we get completely integrable system of linear PDE system by removing redundant terms and adding new integrability conditions. The theorem determining whether a system is completely integrable is given in the paper, and its proof is provided as well. Our algorithm is applicable not only to the linear PDEs with constant coefficients but also to the general case.