Differential characteristic set algorithm for the complete symmetry classification of partial differential equations

被引：0

作者：

特木尔朝鲁 ^{[1
]}

白玉山 ^{[2
]}

机构：

[1] Department of Mathematics,Shanghai Maritime University

[2] College of Science,Inner Mongolia University of Technology

来源：

AppliedMathematicsandMechanics(EnglishEdition) | 2009年 / 30卷 / 05期

关键词：

partial differential equations; symmetry; classification; differential characteristic set;

D O I：

暂无

中图分类号：

O175.2 [偏微分方程];

学科分类号：

070104 ;

摘要：

In this paper,we present a differential polynomial characteristic set algorithm for the complete symmetry classification of partial differential equations(PDEs) with some parameters.It can make the solution to the complete symmetry classification problem for PDEs become direct and systematic.As an illustrative example,the complete potential symmetry classifications of nonlinear and linear wave equations with an arbitrary function parameter are presented.This is a new application of the differential form characteristic set algorithm,i.e.,Wu’s method,in differential equations.

引用

页码：595 / 606

页数：12

共 14 条

[1]

Nearly characteristic set of differential polynomial system. Temuerchaolu,,Gao X.S. Acta Mathematica Sinica,Chinese Series . 2002

[2]

Symmetries and Differential Equations. Bluman G W and Kumei S. Appl. Math. Sci .No 81 Springer ,New York . 1989

[3]

Local and Nonlocal Symmetries for Nonlinear Telegraph Equations. Bluman G W,Temuerchaolu. Journal of Mathematical Physics . 2005

[4]

Basic Principles of Mechanical Theorem Proving in Geometries. Wen-tsün,Wu. Journal of Systems Science and Mathematical Sciences . 1984

[5]

Group Analysis of Di-erential Equations. Ovsiannikov,L.V,(trans.Ames,W.F.). . 1982

[6]

Determination of maximal symmetry groups of classes of dif- ferential equations. Reid,G.J,Wittkoipf,A.D. Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation . 2000

[7]

Arnol’d,V. I. Mathematical Methods of Classical Mechanics . 1978

[8]

On the foundation of algebraic differential geometry. Wu,W. T. Sys Sci & Math Scis . 1989

[9]

An Algorithmic Theory of Reduction of Differential Polynomials System. Temurchaolu. Advances in Mathematics . 2003

[10]

Equation Solving and Mechanical Proving- Solving Problems Based on MMP. Gao,Xiaoshan,Wang,Dingkang,Yang,Hong. . 2006

← 1 2 →