The extended Lotka-Volterra lattice and affine Jacobi varieties of spectral curves

Abstract

Based on the work by Smirnov and Zeitlin, we study a simple realization of the matrix construction of the affine Jacobi varieties. We find that the realization is given by a classical integrable model, the extended Lotka-Volterra lattice. We investigate the integrable structure of the representative for the gauge equivalence class of matrices, which is isomorphic to the affine Jacobi variety, and make use it to discuss the solvability of the model.

17 pages, revised on October 15, 2002

References in corpus (2)

• Cohomologies of Affine Jacobi Varieties and Integrable Systems
• Dual Baxter equations and quantization of Affine Jacobian

Cited by in corpus (1)

• The matrix realization of affine Jacobi varieties and the extended Lotka-Volterra lattice