The matrix realization of affine Jacobi varieties and the extended Lotka-Volterra lattice
نویسنده
چکیده
Abstract: We study the representative for the gauge equivalence class MF related to certain types of N by N monodromy matrices whose entries are polynomials of a spectral parameter z. Let X be the algebraic curve given by the common characteristic equation for MF . Then the representative corresponds to the matrix realization of the affine Jacobi variety of X . When we relate MF to the Lax matrix for a finite dimensional classical dynamical system, this variety becomes the invariant manifold of the system. As the application, we discuss the algebraic completely integrability of the extended Lotka-Volterra lattice with a periodic boundary condition.
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