TY - JOUR AU - Zhang, Yufeng AU - Zhang, Xiangzhi PY - 2017 DA - 2017/03/04 TI - Two kinds of discrete integrable hierarchies of evolution equations and some algebraic-geometric solutions JO - Advances in Difference Equations SP - 72 VL - 2017 IS - 1 AB - With the help of a loop algebra we first present a $(1+1)$-dimensional discrete integrable hierarchy with a Hamiltonian structure and generate a $(2+1)$-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. SN - 1687-1847 UR - https://doi.org/10.1186/s13662-017-1124-3 DO - 10.1186/s13662-017-1124-3 ID - Zhang2017 ER -