摘要：With the help of a loop algebra we first present a ( 1 + 1 ) $(1+1)$ -dimensional discrete integrable hierarchy with a Hamiltonian structure and generate a ( 2 + 1 ) $(2+1)$ -dimensional discrete integrable hierarchy, respectively. Then we obtain a new differential-difference integrable system with three-potential functions, whose algebraic-geometric solution is derived from the theory of algebraic curves, where we construct the new elliptic coordinates to straighten out the continuous and discrete flows by introducing the Abel maps as well as the Riemann-Jacobi inversion theorem.
关键词：discrete integrable system ; elliptic coordinate ; algebro-geometric solution
