  A three-by-three matrix spectral problem for AKNS soliton hierarchy is
proposed and the corresponding Bargmann symmetry constraint involved in Lax
pairs and adjoint Lax pairs is discussed. The resulting nonlinearized Lax
systems possess classical Hamiltonian structures, in which the nonlinearized
spatial system is intimately related to stationary AKNS flows. These
nonlinearized Lax systems also lead to a sort of involutive solutions to each
AKNS soliton equation.
