Involutive characteristic sets of algebraic partial differential equation systems  

作　　者：陈玉福 高小山 

机构地区：[1]Graduate School,Chinese Academy of Sciences,Beijing 100039,China [2]Institute of Systems Science,AMSS,Chinese Academy of Sciences,Beijing 100080,China

出　　处：《Science China Mathematics》2003年第4期469-487,共19页中国科学：数学（英文版）

基　　金：This work was supported in part by a National Key Basic Research Project of China(No.G19980306);the National Natural Science Foundation of China(Grant No.69725002).

摘　　要：This paper presents an algorithm to reduce a nonlinear algebraic partial differential equation system into the involutive characteristic set with respect to an abstract involutive prolongation direction, which covers the existing algorithms based on Riquier method, Thomas method, and Pommaret method. It also provides new algorithms for computing involutive characteristic sets due to the existence of new involutive directions. Experiments show that these new algorithms may be used to significantly reduce the computational steps in Wu-Ritt's characteristic set method for algebraic partial differential equations.This paper presents an algorithm to reduce a nonlinear algebraic partial differential equation system into the involutive characteristic set with respect to an abstract involutive prolongation direction, which covers the existing algorithms based on Riquier method, Thomas method, and Pommaret method. It also provides new algorithms for computing involutive characteristic sets due to the existence of new involutive directions. Experiments show that these new algorithms may be used to significantly reduce the computational steps in Wu-Ritt’s characteristic set method for algebraic partial differential equations.

关 键 词：involutive CHARACTERISTIC set  INTEGRABILITY conditions  ALGEBRAIC PARTIAL differential equation system  Wu-Ritt's CHARACTERISTIC SET method. 

分 类 号：O175[理学—数学]