新型Poisson 括号意义下的无穷维Lie代数注意:本论文已在《力学学报》
1998年30卷3期,307-313页, 1998年5月发表 张宝善, 卢东强,
戴世强 摘要: 本文首先针对DdV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Poisson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。 Infinite-Dimensional Lie Algebra With a New Poisson Bracket Zhang Baoshan, Lu Dongqiang, Dai
Shiqiang Abstract: For the Hamiltonian
formulation of the Korteweg-de Vires equation (KdV equation), C.S. Gardner
defined a Poisson bracket. In this paper a brand-new bracket is defined. It is
easily verified that 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. The project supported by the National Natural Science Foundation of China. 1、浏览PDF格式全文需要使用软件--Abode Acrobat(由于软件较大并常见,我站不提供下载) 2、下载论文全文请点击(612KB)
本站收录的本文作者的其他论文: 1、Hamiltonian Formulation of Nonlinear Water Waves in a Two-Fluid System 3、Free-surface waves and far wakes generated by a floating body in a viscous fluid |
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