偏微分方程(组)完全对称分类微分特征列集算法

特木尔朝鲁; 白玉山

doi:10.3879/j.issn.1000-0887.2009.05.006

偏微分方程(组)完全对称分类微分特征列集算法

doi: 10.3879/j.issn.1000-0887.2009.05.006

特木尔朝鲁¹,
白玉山²

上海海事大学应用数学物理所,上海 200135;2.内蒙古工业大学理学院,呼和浩特 010051

基金项目: 教育部博士点基金资助项目(20070128001);上海市教委支出预算资助项目(2008069);上海市教委科研创新资助项目(09YZ239);内蒙古自然科学基金重点资助项目(200607010103)

详细信息

作者简介:
特木尔朝鲁(1962- ),男,内蒙古人,蒙古族,教授,博士(联系人.Tel:+86-21-38282233;E-mail:tmchaolu@dbc.shmtu.edu.cn).

中图分类号: O152.5;O175.2
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出版历程
- 收稿日期: 2008-06-01
- 修回日期: 2009-03-09
- 刊出日期: 2009-05-15

Differential Characteristic Set Algorithm for the Complete Symmetry Classification of (Partial) Differential Equations

Temuer Chaolu¹,
BAI Yu-shan²

Mathematics Department, Shanghai Maritime University, Shanghai 200135, P. R. China;

摘要

摘要: 给出了一个确定含参数偏微分方程(组)的完全对称分类微分特征列集算法,该算法能够直接、系统地确定偏微分方程(组)的完全对称分类．用给出的算法获得了含任意函数类参数的线性和非线性波动方程完全势对称分类．这也是微分形式特征列集算法(微分形式吴方法)在微分方程领域中的新应用．
- 偏微分方程 /
- 对称 /
- 分类 /
- 特征列集
Abstract: A differential polynomial characteristic set algorithm for the complete symmetry classification of (partial) differe ntial equations with some parameters was given, which made the solution of the complete symmetry classification problem for (partial) differential equations become direct and systematic. As an illustrative example, the complete potential symmetry classifications of nonlinear and linear wave equations with an arbitrary function parameter were presented. This is a new application of differential form characteristic set algrithmc (differential form Wu.s method) in field of differential equations.
- partial differential equations /
- symmetry /
- classification /
- differential characteristic set

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参考文献(14)

[1]	Olver P J.Applications of Lie Groups to Differential Equations[M].New York/Berlin: Springer-Verlag, 1991.
[2]	Bluman G W,Kumei Sukeyuki. Symmetries and Differential Equations[M](App Math Sci,81). Beijing:Springer-Velag,World Publishing Corp, 1991.
[3]	Ovsiannikov L W.Group Analysis of Differential Equations[M].transl Ames W F.New York/London:Academic Press, 1982.(English version)
[4]	Arnol'd V I.Mathematical Methods of Classical Mechanics[M].New York: Springer-Verlag, 1978.
[5]	Bluman G W,Chaolu Temuer,Sahadevan R.Local and nonlocal symmetries for nonlinear telegraph equations[J].J Math Phys,2005,46(2):1-12.
[6]	Clarkson P A,Mansfield E L. Open problems in symmetry analysis[A].In:Leslie J A,Robart T,Eds.Geometrical Study of Differential Equations[C].285.Contemporary Mathematics Series.Providence, RI:A M S,2001,195-205.
[7]	Reid G J,Wittkoipf Allan D.Determination of maximal symmetry groups of classes of differential equations[A].In:Proceedings of the 2000 International Symposium on Symboic and Algebraic Computation[C].St Andrews, Scotland,New York,NY:ACM,2000,272-280.
[8]	高小山,王定康,杨宏.方程求解与机器证明——基于MMP的问题求解[M].北京:科学出版社,2006.
[9]	吴文俊.初等几何定理机器证明的基本原理[J].系统科学与数学，1984,4(3):207-235.
[10]	WU Wen-tsun.Mathematics Mechanization[M].Beijing/Dordrecht/Boston/London: Science Press,Kluwer Academic Publishers, 2000.
[11]	WU Wen-tsun. On the foundation of algebraic differential geometry[J].J Systems Sci & Comp,1989,2(4): 289-312.
[12]	朝鲁,高小山.微分多项式系统的近微分特征列集[J].数学学报,2002,45(6): 1041-1050.
[13]	Temuer Chaolu.An algorithmic theory of reduction of differential polynomial system[J].Adv Math,2003,32(2):208-220.
[14]	Baikov V A, Gazizov R A,Ibragimov N H.Approximate group analysis of nonlinear equationutt-(f(u)ux)x+[KG*4]. (u)ut=0[J].Differentsialinge,Uravnenign,1988,24(7): 1127-1138.

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偏微分方程(组)完全对称分类微分特征列集算法

doi: 10.3879/j.issn.1000-0887.2009.05.006

作者简介:
特木尔朝鲁(1962- ),男,内蒙古人,蒙古族,教授,博士(联系人.Tel:+86-21-38282233;E-mail:tmchaolu@dbc.shmtu.edu.cn).

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Differential Characteristic Set Algorithm for the Complete Symmetry Classification of (Partial) Differential Equations

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偏微分方程(组)完全对称分类微分特征列集算法

doi: 10.3879/j.issn.1000-0887.2009.05.006

作者简介: 特木尔朝鲁(1962- ),男,内蒙古人,蒙古族,教授,博士(联系人.Tel:+86-21-38282233;E-mail:tmchaolu@dbc.shmtu.edu.cn).

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出版历程

Differential Characteristic Set Algorithm for the Complete Symmetry Classification of (Partial) Differential Equations

计量

出版历程

目录

作者简介:
特木尔朝鲁(1962- ),男,内蒙古人,蒙古族,教授,博士(联系人.Tel:+86-21-38282233;E-mail:tmchaolu@dbc.shmtu.edu.cn).