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- Title
Algebro-Geometric Integration of the Modified Belov—Chaltikian Lattice Hierarchy.
- Authors
Geng, Xianguo; Wei, Jiao; Zeng, Xin
- Abstract
Using the Lenard recurrence relations and the zero-curvature equation, we derive the modified Belov—Chaltikian lattice hierarchy associated with a discrete 3×3 matrix spectral problem. Using the characteristic polynomial of the Lax matrix for the hierarchy, we introduce a tri gonal curve Km−2 of arithmetic genus m−2. We study the asymptotic properties of the Baker—Akhiezer function and the algebraic function carrying the data of the divisor near P ∞ 1 , P ∞ 2 , P ∞ 3 , and P0 on Km−2. Based on the theory of trigonal curves, we obtain the explicit theta-function representations of the algebraic function, the Baker—Akhiezer function, and, in particular, solutions of the entire modified Belov—Chaltikian lattice hierarchy.
- Subjects
THETA functions; DIVISOR theory; ALGEBRAIC functions; HIERARCHIES
- Publication
Theoretical & Mathematical Physics, 2019, Vol 199, Issue 2, p675
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1134/S0040577919050052