Volume 7, Issue 1, February 2000, Pages 57 - 72
On Exact Solution of a Classical 3D Integrable Model
- S.M. SERGEEV
- Corresponding Author
- S.M. SERGEEV
Available Online 13 December 2006.
- https://doi.org/10.2991/jnmp.2000.7.1.5How to use a DOI?
- 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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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 - 1776-0852 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 -