Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11026234 | Chaos, Solitons & Fractals | 2018 | 11 Pages |
Abstract
A hierarchy of discrete nonlinear evolution equations associated with a discrete 3ââ¯Ãâ¯â3 matrix spectral problem with two potentials is proposed by means of the Lenard recursion equations and zero-curvature equation. Based on the characteristic polynomial of Lax matrix for the hierarchy, we introduce a trigonal curve and study the properties of the corresponding three-sheeted Riemann surface, especially including arithmetic genus, holomorphic differentials. Base on the essential properties of the meromorphic functions Ï2, Ï3 and the Baker-Akhiezer function Ï1, and their asymptotic behavior, we obtain Riemann theta function solutions of the entire discrete integrable hierarchy.
Keywords
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
Xianguo Geng, Xin Zeng, Jiao Wei,