Journal of Nonlinear Mathematical Physics

Volume 7, Issue 1, February 2000, Pages 57 - 72

On Exact Solution of a Classical 3D Integrable Model

Authors
S.M. SERGEEV
Corresponding Author
S.M. SERGEEV
Available Online 13 December 2006.
DOI
https://doi.org/10.2991/jnmp.2000.7.1.5How to use a DOI?
Abstract
We investigate some classical evolution model in the discrete 2+1 space-time. A map, giving an one-step time evolution, may be derived as the compatibility condition for some systems of linear equations for a set of auxiliary linear variables. Dynamical variables for the evolution model are the coefficients of these systems of linear equtions. Determinant of any system of linear equations is a polynomial of two numerical quasimomenta of the auxiliary linear variables. For one, this determinant is the geerating functions of all integrals of motion for the evolution, and on the other hand it defines a high genus algebraic curve. The dependence of the dynamical variables on the space-time point (exact solution) may be expressed in terms of theta functions on the jacobian of this curve. This is the main result of our paper.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
7 - 1
Pages
57 - 72
Publication Date
2006/12
ISSN
1402-9251
DOI
https://doi.org/10.2991/jnmp.2000.7.1.5How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - S.M. SERGEEV
PY  - 2006
DA  - 2006/12
TI  - On Exact Solution of a Classical 3D Integrable Model
JO  - Journal of Nonlinear Mathematical Physics
SP  - 57
EP  - 72
VL  - 7
IS  - 1
SN  - 1402-9251
UR  - https://doi.org/10.2991/jnmp.2000.7.1.5
DO  - https://doi.org/10.2991/jnmp.2000.7.1.5
ID  - SERGEEV2006
ER  -