Abstract: It is important to search for new integrable equations hierarchies in soliton theory. First, a new equations hierarchy was constructed. Taking use of higherdimension Lie algebra A2 and the corresponding loop algebra [AKA~]2, it was proved that the equations hierarchy is Lax integrable. Then, the biHamiltonian structures of the Lax integrable hierarchy were constructed by making use of the trace identity. Finally, the infinitely conserved densities for the equations hierarchy was obtained and it was proved that the Lax equations hierarchy is Liouville integrable.

Key words: Lie algebra , Integrable system , Hamiltonian structure

摘要： 寻找新的可积方程族在孤立子理论中是十分重要的。首先,构造了一个新的方程族,利用高维Lie代
数A2 及其相应的loop代数煋A2,证明了此方程族是Lax可积的。其次,利用迹恒等式构造了Lax可积方程族的双
Hamilton结构。最后,获得了此方程族的无穷多守恒密度,证明了此方程族为Liouville可积的。

关键词: Lie代数 , 可积系统 , Hamilton结构