An integrable Hamiltonian hierarchy, a high-dimensional loop algebra and associated integrable coupling system

• 来源期刊: 中国物理(英文版)
• 关键词: loop algebra integrable system Hamiltonian structure constrained flow
• 年，卷（期）: 2003,（11）
• 页码范围: 1194-1201
• 页数: 8页
• 语种: 英文

摘要

A subalgebra of loop algebra A2 is established. Therefore, a new isospectral problem is designed. By making use of Tu's scheme, a new integrable system is obtained, which possesses bi-Hamiltonian structure. As its reductions,a formalism similar to the well-known Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and a generalized standard form of the Schrodinger equation are presented. In addition, in order for a kind of expanding integrable system to be obtained, a proper algebraic transformation is supplied to change loop algebra A2 into loop algebra A1. Furthermore,a high-dimensional loop algebra is constructed, which is different from any previous one. An integrable coupling of the system obtained is given. Finally, the Hamiltonian form of a binary symmetric constrained flow of the system obtained is presented.