一个新的Liouville可积方程族及其双Hamilton结构

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。

A New Liouville Integrable Hierarchy and Its Bi-Hamiltonian Structure

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 A2 and the corresponding loop algebra A2, 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.