A NEW INTEGRABLE SYMPLECTIC MAP ASSOCIATED WITH LATTICE SOLITON-EQUATIONS

A method is developed that extends the nonlinearization technique to t he hierarchy of lattice soliton equations associated with a discrete 3 x 3 matrix spectral problem. A new integrable symplectic map and its involutive system of conserved integrals are obtained by the nonlinear ization of spatial parts and the time parts of Lax pairs and their adj oint Lax pairs of the hierarchy. Moreover, the solutions of the typica l system of lattice equations in the hierarchy are reduced to the solu tions of a system of ordinary differential equations and a simple iter ative process of the symplectic map. (C) 1996 American Institute of Ph ysics.