新型Poisson括号意义下的无穷维Lie代数
INFINITE DIMENSIONAL LIE ALGEBRA WITH A NEW POISSON BRACKET 1)
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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．
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关键词:
- KdV方程 /
- Hamilton形式 /
- 第一积分 /
- Poisson括号 /
- 无穷维Lie代数
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 dimension... -
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