Algebro-geometric Constructions of Quasi Periodic Flows of the Discrete Self-dual Network Hierarchy and Applications

Abstract

In this paper we obtain the discrete integrable self-dual network hierarchy associated with a discrete spectral problem. On the basis of the theory of algebraic curves, the continuous flow and discrete flow related to the discrete self-dual network hierarchy are straightened using the Abel-Jacobi coordinates. The meromorphic function and the Baker-Akhiezer function are introduced on the hyperelliptic curve. Quasi-periodic solutions of the discrete self-dual network hierarchy are constructed with the help of the asymptotic properties and the algebra-geometric characters of the meromorphic function, the Baker-Akhiezer function and the hyperelliptic curve.