Some Evolution Hierarchies Derived from Self-dual Yang-Mills Equations

• 作者: 张玉峰 韩耀宗
• 来源期刊: 理论物理通讯：英文版
• 学科: 数学
• 关键词: 演化方程 Hamilton结构 扩展可积模型 loop代数 演变 层次结构 线性代数 泊松结构
• 年，卷（期）: 2011,（11）
• 页码范围: 856-872
• 页数: 17页
• 分类号: O175.29|O411.1
• 语种: 英文

摘要

We develop in this paper a new method to construct two explicit Lie algebras E and F. By using a loop algebra E of the Lie algebra E and the reduced self-dual Yang-Mills equations, we obtain an expanding integrable model of the Giachetti-Johnson （G J） hierarchy whose Hamiltonian structure can also be derived by using the trace identity. This provides a much simplier construction method in comparing with the tedious variational identity approach. Furthermore, the nonlinear integrable coupling of the GJ hierarchy is readily obtained by introducing the Lie algebra gN. As an application, we apply the loop algebra E of the Lie algebra E to obtain a kind of expanding integrable model of the Kaup-Newell （KN） hierarchy which, consisting of two arbitrary parameters a and β, can be reduced to two nonlinear evolution equations. In addition, we use a loop algebra F of the Lie algebra F to obtain an expanding integrable model of the BT hierarchy whose Hamiltonian structure is the same as using the trace identity. Finally, we deduce five integrable systems in R3 based on the self-dual Yang-Mills equations, which include Poisson structures, irregular lines, and the reduced equations.

作者信息

序号	姓名	单位	发文数	被引次数	H指数	G指数
1	张玉峰		21	32	4.0	4.0
2	韩耀宗		1	0	0.0	0.0