中国科学院研究生院学报2006，Vol.23Issue(1)：7-22,16.
代数偏微分方程组的对合特征集方法分析
Analysis of the Involutive Characteristic Set Method for Algebraic PDE Systems
摘要
Abstract
Based on Wu-Ritt's characteristic set method and V. Gerdet's involutive division method, we defined the involutive characteristic set (ICS) for a set of non-linear PDEs with respect to a general involutive direction. The ICS method depends on two factors: the prolongation direction and the variable ordering. In this paper, we report an implementation of the ICS method and use it to solve a large set of PDE systems raised from the computation of symmetric groups for PDEs. Based on the experiments, we try to select the best prolongation direction and the variable ordering for the ICS algorithm.关键词
对合特征集/可积条件/代数偏微分方程组/Wu-Ritt特征集方法Key words
involutive characteristic set/integrability conditions/algebraic partial differential equation system/Wu-Ritt's characteristic set method分类
数理科学引用本文复制引用
孟晓辉,陈玉福..代数偏微分方程组的对合特征集方法分析[J].中国科学院研究生院学报,2006,23(1):7-22,16.基金项目
supported in part by a National Key Basic Research Project of China(G19980306) （G19980306）
