Abstract
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 ϕ, Baker-Akhiezer vector \(\bar \psi \), and hyperelliptic curve ɛN according to whose asymptotic properties and the algebro-geometric characters we construct quasiperiodic solutions of the discrete Chen-Lee-Liu hierarchy.
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