Quasiperiodic solutions of the discrete Chen-Lee-Liu hierarchy

Using the Lax matrix and elliptic variables, we decompose the discrete Chen-Lee-Liu hierarchy into solvable ordinary differential equations. Based on the theory of the algebraic curve, we straighten the continuous and discrete flows related to the discrete Chen-Lee-Liu hierarchy in Abel-Jacobi coordinates. We introduce the meromorphic function ?, Baker-Akhiezer vector \(\bar \psi \) , and hyperelliptic curve ?_N according to whose asymptotic properties and the algebro-geometric characters we construct quasiperiodic solutions of the discrete Chen-Lee-Liu hierarchy.