拟线性三阶演化方程的初步群分类

Preliminary Group Classification of Quasi-Linear Third Order Evolution Equations

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2、9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.

Group classification of quasi-linear third order 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. Furthermore,it is also shown that there exist two,five,twenly-nine and twenty-six inequivalent third order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.