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

Abstract

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 $\varphi$, the Baker-Akhiezer vector $\bar{\psi }$ 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 $\varphi ,\bar{\psi }$ and ${\mathcal{K}}_N$.

This paper has been withdrawn by the author. In order submit the paper to the SIGMA, I submit the paper to arXiv, but The SIGMA think this paper is not suitable for consideration in SIGMA So I hope withdrawn arXiv paper 1304.1607