A new integrable symplectic map of Neumann type

The nonlinearization approach is generalized to the case of the Neumann con straint associated with a discrete 3 x 3 matrix eigenvalue problem. A new s ymplectic map of the Neumann type is obtained by nonlinearization of the di screte eigenvalue problem and its adjoint one. A scheme for generating the involutive system of conserved integrals of the symplectic map is proposed, by which the symplectic map of the Neumann type is further proved to compl etely integrable. As an application. the calculation of solutions for the h ierarchy of lattice soliton equations connected to the discrete eigenvalue problem is reduced to the solutions of a system of ordinary differential eq uations plus a simple iterative process of the symplectic map of the Neuman n type.