Algebro-geometric solutions of the discrete Ragnisco-Tu hierarchy

A hierarchy of differential-difference equations is derived, which are composed of the positive and negative Ragnisco–Tu flows. Based on the theory of algebraic curve, the continuous flow is straightened in the Abel–Jacobi coordinates. The meromorphic function ϕ, the Baker–Akhiezer vector ψ¯ and the hyperelliptic curve KNKN are introduced, by which algebro-geometric solutions of the discrete Ragnisco–Tu hierarchy are constructed according to the asymptotic properties and the algebro-geometric characters of ϕ, ψ¯ and KNKN.