Adjoint symmetry constraints of the vector KN equations and their integrable coupling system

In this paper we present a soliton hierarchy of vector KN (Kaup-Newell) equations by using an arbitrary order matrix spectral problem, along with its bi-Hamiltonian formulation. Then, adjoint symmetry constraints are presented for manipulating binary nonlinearization for the associated arbitrary order matrix spectral problem. The resulting spatial and temporal constrained flows are shown to provide integrable decompositions of the vector KN equations. Finally, a class of integrable coupling systems of the vector KN soliton equations is obtained through enlarging the spectral problem.