This article is cited in 12 papers

The $r$-Matrix and an Algebraic-Geometric Solution of the AKNS System

Qiao Zhijun<sup>abc

a</sup> Los Alamos National Laboratory
^b Fudan University
^c Universität Kassel

Abstract: We construct an approach to finite-dimensional integrable systems with nonlinear evolution equations from the standpoint of the $r$-matrix and an algebraic-geometric solution, illustrating the method with the well-known AKNS equation. We present the $r$-matrix of the constrained AKNS flow and obtain the algebraic-geometric solution of the AKNS equation.

DOI: 10.4213/tmf476

 English version: Theoretical and Mathematical Physics, 2001, 127:3, 827–834

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