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物理学报. 2001, 50(7): 1232-1236.
doi: 10.7498/aps.50.1232.
新的Lax可积发展方程族及其无限维双-哈密顿结构
- 收稿日期: 2000-11-13
- 刊出日期: 2001-07-20
摘要: 基于一个新的具有三个位势函数(q,r,s)的等谱问题,获得了一族新的含有一个任意函数的Lax可积发展方程.特别地,当位势函数s取不同的函数时,这个方程族约化为若干类型的方程组,进一步利用迹恒等式,给出了这些方程组的双哈密顿结构,并且证明它们是Liouville可积的.此外,给出了守恒密度和对称.
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关键词:
- 等谱问题 /
- 哈密顿结构 /
- Lax可积 /
- Liouville可积
English Abstract
NEW LAX INTEGRABLE HIERARCHY OF EVOLUTION EQUATIONS AND ITS INFINITE-DIMENSIONAL BI-HAMILTONIAN STRUCTURE
- Received Date:
13 November 2000
- Published Online:
20 July 2001
Abstract: Based on a new isospectral problem with three potential functions (q,r,s),a new Lax integrable hierarchy of evolution equations with an arbitrary function is obtained in this paper.When the potential,s,is put into differential functions,the hierarchy of equations can reduce to several kinds of systems of equations.By using the trace identity,their bi-Hamiltonian structures are given,and it is shown that they are integrable in the Liouville's sense.Moreover,the conserved densities and symmetries are also found.
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