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 and the finite dimensional Hamiltonian systems are Liouville integrable.
Xiangrong Wang. Xiaoen Zhang. Peiyi Zhao. "Binary Nonlinearization for AKNS-KN Coupling System." Abstr. Appl. Anal. 2014 (SI31) 1 - 12, 2014. https://doi.org/10.1155/2014/253102