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新型Poisson括号意义下的无穷维Lie代数
引用本文:张宝善,卢东强,戴世强.新型Poisson括号意义下的无穷维Lie代数[J].力学学报,1998,30(3):307-313.
作者姓名:张宝善  卢东强  戴世强
作者单位:上海大学上海市应用数学和力学研究所
摘    要:本文首先针对KdV方程的Hamilton形式,建立一种比较容易验证的新型Poisson括号和无穷维Lie代数.其次,研究KdV方程的Hamilton形式的第一积分与新型Poison括号的关系,得到判定第一积分的充分必要条件.最后,构造KdV方程的第一积分.

关 键 词:KdV方程  无穷维  分析力学  P-括号  李代数

INFINITE DIMENSIONAL LIE ALGEBRA WITH A NEW POISSON BRACKET 1)
Zhang Baoshan,Lu Dongqiang,Dai Shiqiang.INFINITE DIMENSIONAL LIE ALGEBRA WITH A NEW POISSON BRACKET 1)[J].chinese journal of theoretical and applied mechanics,1998,30(3):307-313.
Authors:Zhang Baoshan  Lu Dongqiang  Dai Shiqiang
Abstract:For the Hamiltonian formulation of the Korteweg de Vires equation (KdVequation), C.S. Gardner defined a Poisson bracket. In this paper a brand new bracket is defined. It is easily verified that the new bracket possesses three properties of the Poisson bracket, bilinearity,skew symmetry, Jacobi identity. The new Poisson bracket has a close connection with C.S. Gardner's definition. In the framework of the new Poisson bracket, all the first integrals of the KdV equation constitute an infinite dimensional Lie algebra. Then the necessary and sufficient conditions for identifying the first integrals are obtained. Finally,the method for finding first integrals of KdV equation is investigated.
Keywords:KdV equation  Hamilton formulation  first integral  Poisson bracket  infinite  dimensional Lie algebra  
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