Lie-Poisson Structure For The Nonlinearized Spectral Problem Of The AKNS N=2 Hierarchy

This paper is based on the adjoint eigenvalue problem associated with the AKNS N=2 hierarchy, then the finite-dimensional Hamiltonian system with Lie-Poisson structure in Lax form is obtained by the nonlinearized procedure, the integrability of the Lie-Poisson Hamilton system is thus discussed, moreover, the corresponding flows is straightened in the framework of the Hamilton-Jacobi theory.