Quantization And Darboux Transformation Of The Finite Dimensional Integrable Systems Corresponding To AKNS Hierarchy

In this paper,we study the finite dimensional integrable systems corresponding to AKNS hierarchy from two aspects.Firstly,we use the quantization method to give the quantization forms of the stationary AKNS system,quantum integrals and -matrix relationship in three different coordinates.Secondly,we apply the Darboux transformation of AKNS hierarchy to the stationary system and Lie-Poisson structure,the results show that the stationary AKNS system keeps the conservative integral and Lie-Poisson structure unchanged.