一个李代数及其相应的可积哈密顿系统

A Lie algebra and corresponding integrable Hamiltonian system

在理论上如何构造更好的可积模型,特别是无穷维哈密顿系统是可积系统研究工作的主要内容之一。本文构造了一个李代数并由此生成相应的圈代数,从而建立了一个适当的等谱问题,利用屠格式得到了一族拉克斯意义下的可积系统,根据迹恒等式得到了这个非线性可积系统的哈密顿结构。

How to construct a better integrable model in theory,especially the infinite dimensional Hamiltonian system,is one of the main contents of the integrable system. A Lie algebra and its loop algebra are established,from which an isospectral problem is defined. By using Tu-model,a nonlinear integrable hierarchy in the sense of Lax is obtained. Moreover,the trace identity over the corresponding loop algebra is used to furnish the Hamiltonian structure for the resulting nonlinear integrable system.