(2+1)维KdV族的可积耦合及其哈密顿结构

Integrable Couplings of the (2+1)-Dimensional KdV Hierarchy and its Hamiltonian Structure

首先构造了一个loop代数,根据(2+1)维零曲率方程计算得到(2+1)维KdV族的可积耦合,然后通过二次型恒等式得到它的哈密顿结构.展示的方法新颖简便,可以用于其它许多方程族.

A loop algebra is constructed, whose subalgebra can be used to present a lax pair. Using the （2 ＋ 1 ） -dimensional zero curvature equation, integrable coupling of the （ 2 ＋ 1 ） -dimensional hierarchy is generated. Further more, the Hamilton ian structure of its integrable couplings is worked out by using of the quadratic-form identity, which is of Liouville intergrable. The method mentioned can be widely used to other soliton hierarchies.