On quasi-periodic solutions of the discrete Chen-Lee-Liu hierarchy

Resorting to the Lax matrix and elliptic variables, the discrete Chen-Lee-Liu hierarchy is decomposed into solvable ordinary differential equations. Based on the theory of algebraic curve, the continuous flow and discrete flow related to the discrete Chen-Lee-Liu hierarchy are straightened under the Abel-Jacobi coordinates. The meromorphic function $ϕ$, the Baker-Akhiezer vector $\barψ$ and the hyperelliptic curve $\mathcal{K}_N$ are introduced, by which quasi-periodic solutions of the discrete Chen-Lee-Liu hierarchy are constructed according to the asymptotic properties and the algebro-geometric characters of $ϕ,\ \barψ$ and $\mathcal{K}_N$.

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