Binary Nonlinearization for AKNS-KN Coupling System

Abstract

The AKNS-KN coupling system is obtained on the base of zero curvature equation by enlarging the spectral equation. Under the Bargmann symmetry constraint, the AKNS-KN coupling system is decomposed into two integrable Hamiltonian systems with the corresponding variables $x,t_n$ and the finite dimensional Hamiltonian systems are Liouville integrable.