拟线性三阶演化方程的初步群分类

黄定江; 张鸿庆

拟线性三阶演化方程的初步群分类

黄定江^1,2,
张鸿庆²

1.
华东理工大学数学系,上海 200237;2.大连理工大学应用数学系,辽宁大连 116024

基金项目: 国家重点基础发展规划(“973”)资助项目(2004CB318000)

详细信息

作者简介:
黄定江(1981- ),男,江西上饶人,博士(Tel:+86-21-64253147;E-mail:hdj8116@163.com);张鸿庆,教授(联系人.Tel:+86-411-84709062;E-mail:zhanghq@dlut.edu.cn).

中图分类号: O175.24；O175.29；O152.5
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出版历程
- 收稿日期: 2008-06-24
- 修回日期: 2008-12-17
- 刊出日期: 2009-03-15

Preliminary Group Classification of Quasi-Linear Third Order Evolution Equations

HUANG Ding-jiang^1,2,
ZHANG Hong-qing²

1.
Department of Mathematics, East China University of Science and Technology, Shanghai 200237, P. R. China;

摘要

摘要: 利用古典无穷小算法、等价性变换技巧和有限维抽象李代数的分类理论，给出了一般拟线性三阶演化方程在半单和一维至四维可解李代数下不变的群分类．证明了只存在3个不等价的方程在三维单李代数下不变,而且进一步证明在所有半单李代数下不变的不等价方程只有这3个．另外,还证明了存在2个、5个、29个和26个不等价的方程，分别在一维至四维可解李代数下不变．
- 拟线性三阶演化方程 /
- 群分类 /
- 古典无穷小算法 /
- 等价群 /
- 抽象李代数
Abstract: Group classification of quasilinear thir dorder evolution equations is performed by using the classical infinitesimal Lie method, the technique of equivalence transformations and the theory of classification of abstract low-dimensional Lie algebras. It is indicated that there are three equations admitting simple Lie algebras of dimension three. What's more, all the inequivalent equations admitting simple Lie algebra are nothing but them. Further more, it is also shown that there exist two, five, twenty-nine and twenty-six inequivalent third or der nonlinear evolution equations a dmitting one-, two, three, and fourdimensional solvable Lie algebras, respectively.
- quasi-linear third order evolution equations /
- group classification /
- classical infinitesimal Lie method /
- equivalence transfor mations group /
- abstract Lie algebras

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参考文献(33)

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拟线性三阶演化方程的初步群分类

作者简介:
黄定江(1981- ),男,江西上饶人,博士(Tel:+86-21-64253147;E-mail:hdj8116@163.com);张鸿庆,教授(联系人.Tel:+86-411-84709062;E-mail:zhanghq@dlut.edu.cn).

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Preliminary Group Classification of Quasi-Linear Third Order Evolution Equations

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留言板

拟线性三阶演化方程的初步群分类

作者简介: 黄定江(1981- ),男,江西上饶人,博士(Tel:+86-21-64253147;E-mail:hdj8116@163.com);张鸿庆,教授(联系人.Tel:+86-411-84709062;E-mail:zhanghq@dlut.edu.cn).

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出版历程

Preliminary Group Classification of Quasi-Linear Third Order Evolution Equations

计量

出版历程

目录

作者简介:
黄定江(1981- ),男,江西上饶人,博士(Tel:+86-21-64253147;E-mail:hdj8116@163.com);张鸿庆,教授(联系人.Tel:+86-411-84709062;E-mail:zhanghq@dlut.edu.cn).