Algebro-Geometric Integration of the Modified BelovChaltikian Lattice Hierarchy

Using the Lenard recurrence relations and the zero-curvature equation, we derive the modified BelovChaltikian lattice hierarchy associated with a discrete 3x3 matrix spectral problem. Using the characteristic polynomial of the Lax matrix for the hierarchy, we introduce a tri gonal curve Km-2 of arithmetic genus m-2. We study the asymptotic properties of the BakerAkhiezer function and the algebraic function carrying the data of the divisor near P1, P2, P3, and P-0 on Km-2. Based on the theory of trigonal curves, we obtain the explicit theta-function representations of the algebraic function, the BakerAkhiezer function, and, in particular, solutions of the entire modified BelovChaltikian lattice hierarchy.