Preliminary group classification of quasilinear third-order evolution equations  

作　　者：黄定江 张鸿庆 

机构地区：[1]Department of Mathematics,East China University of Science and Technology [2]Department of Applied Mathematics, Dalian University of Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2009年第3期275-292,共18页应用数学和力学（英文版）

基　　金：supported by the National Key Basic Research Project of China (973 Program)(No. 2004CB318000)

摘　　要：Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six non- equivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six non- equivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.

关 键 词：quasilinear third-order evolution equations group classification classical infinitesimal Lie method equivalence transformation group abstract Lie algebras 

分 类 号：O175.24[理学—数学]