Algebro-Geometric Solutions for a Discrete Integrable Equation

الملخص EN

With the assistance of a Lie algebra whose element is a matrix, we introduce a discrete spectral problem.

By means of discrete zero curvature equation, we obtain a discrete integrable hierarchy.

According to decomposition of the discrete systems, the new differential-difference integrable systems with two-potential functions are derived.

By constructing the Abel-Jacobi coordinates to straighten the continuous and discrete flows, the Riemann theta functions are proposed.

Based on the Riemann theta functions, the algebro-geometric solutions for the discrete integrable systems are obtained.