超AKNS方程族和AKNS方程族的一致性探究

Research on Super AKNS Hierarchy and AKNS Hierarchy's Uniform

对一个与3×3的LAX对相联系的超AKNS方程族,通过遗传算子φ,找到了方程族的K对和τ对称.进一步,导出了超AKNS方程族中任一个方程的对称所构建的Lie代数结构.通过比较,超AKNS方程族和AKNS方程族的对称及其Lie代数结构,发现他们的一致性.

In this paper, the K symmetry and r symmetry for the super Dirac hierarchy, which is associated with a 3 × 3 Lax pair, are found by using the hereditary operator φ. Moreover, the Lie algebra construction of the symmetries for any one equation of the hierarchy is de- rived. Specially, by contrast the symmetry and Lie algebra construction for the super AKNS hierarchy and AKNS hierarchy, we found the super AKNS hierarchy and AKNS hierarchy have uniform symmetry and Lie algebra construction.