Decomposition And Liouville Integrability Of Discrete Kaup-Newell Equations

A discrete Kaup-Newell equation is obtained with the help of the finite-order expan-sion. Neumann constraint is obtained through the Lax pair nonlinearization technique together with a symplectic map S. The Liouville integrability of the symplectic map is proved by using the generating function and the quasi-Abel-Jacobi coordinates. Finally, with the knowledge of algebraic curve and Abel-Jacobi coordinates, the straightening out of the flows is proposed.