2+1维JM族的可积耦合、Hamilton结构及多分量JM族

Integrable Couplings of the (2+1)-dimensional JM Hierarchy and Its Hamiltonian Structure as well as the Multi-component JM Hierarchy

由自对偶的Yang-M ills方程推导出了2+1维的JM方程族.借助于一个适当的loop代数,利用二次型迹恒等式求出了其Ham ilton结构,并证明该方程族是Li-ouville可积的,最后又通过一个新的代数系统得到了多分量JM族.这种方法具有普遍性,可应用于其他方程族.

A （2 ＋ 1 ） -dimensional JM hierarchy is generated from one of reduced equations of self-dual Yang-Mills equatinos. With the help of a proper loop algebra, the Hamiltonian structure of its expanding integrable model（actually, its integrable couplings）is put out by using the quadratic-form identity, which is Liouville intergrable. Which is more, a corresponding multi-component JM hierarchy is given. The method this paper mentioned can be widely used to other soliton hierarchies.