经典李代数D_r上推广的Toda力学系统

Generalized Toda Mechanics Associated with Classical Lie Algebras D_r

根据经典李代数Dr 根系的特点构造Laxpair ,得到李代数Dr 上推广的Toda链 (这些链用一组有序整数 (m ,n)表示 ,m、n分别表示正、负根的级数 ) ,并给出m ,n≤ 3时系统的运动方程、哈密顿量以及泊松括号的具体形式 .

In this paper, we construct the Lax pair of classical Lie algebra D r according to the characteristic of its root system, and get a family of integrable generalizations of Toda mechanics (labeled by a pair of ordered integers (m,n), m,n denote the order of positive and negative roots respectively). We aiso provide the explicit equations of motion, the Hamiltonian and the Poission brackets corresponding to the case of m,n≤3.