Solutions of a discrete integrable hierarchy by straightening out of its continuous and discrete constrained flows

From the isospectral problem which we design, a (1+1)-dimensional discrete integrable hierarchy is generated with the help of a loop algebra. After that we get a differential-difference integrable system with two potential functions. Finally, the algebro-geometric solution of the integrable system is obtained by straightening out the continuous and discrete flow and utilizing the Riemann-Jacobi inversion theorem.