On Exact Solution of a Classical 3D Integrable Model

DOI

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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - S.M. Sergeev
PY  - 2000
DA  - 2000/02/01
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  - 10.2991/jnmp.2000.7.1.5
ID  - Sergeev2000
ER  -