Loop代数L(D_r)上的推广Toda力学系统研究

Study on Generalized Toda Mechanics System with Loop Algebra L(D_r)

对Loop代数L(Dr)上具有长程相互作用的Toda力学系统进行推广 ,用一组有序整数对 (X ,Y)来表示Toda链 ,构造出Loop代数L (Dr)的LaxPair,并给出了系统在 (3,2 )Toda链情况下的运动方程和Hamiltonian结构 .在此模型中 ,标准的Toda变量之间和附加的坐标变量之间的泊松括号都非零 ,部分附加的坐标变量之间的泊松结构构成李代数 .

In this paper,we generalize the Toda mechanics system with long range interaction to the case of Loop algebra L(D r).By using a pair of ordered positive integer (X,Y) to describe Toda chains,we extract the equation of motion and the Hamiltonian structure of this system for (3,2) Toda chain.It turns out that both extra coordinates and standard Toda variables are Poisson non-commutative in the case of nontrivial generalization,and for some case,extra variables appear linearly on the right hand side of the Poisson bracket.