An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems

Abstract

An explicit symmetry constraint is proposed for the Lax pairs and the adjoint Lax pairs of AKNS systems. The corresponding Lax pairs and adjoint Lax pairs are nonlinearized into a hierarchy of commutative, finite-dimensional integrable Hamiltonian systems in the Liouville sense and thus an involutive representation of solutions of AKNS systems is obtained. The purpose of this Letter is to elucidate that the nonlinearization method (i.e. a kind of symmetry constraint method) of integrable systems can be applied to the Lax pairs and the adjoint Lax pairs associated with integrable systems.