Quasi-periodic solutions of the Belov–Chaltikian lattice hierarchy

Abstract

Utilizing the characteristic polynomial of Lax matrix for the Belov–Chaltikian (BC) lattice hierarchy associated with a [Formula: see text] discrete matrix spectral problem, we introduce a trigonal curve with three infinite points, from which we establish the associated Dubrovin-type equations. The essential properties of the Baker–Akhiezer function and the meromorphic function are discussed, that include their asymptotic behavior near three infinite points on the trigonal curve and the divisor of the meromorphic function. The Abel map is introduced to straighten out the continuous flow and the discrete flow in the Jacobian variety, from which the quasi-periodic solutions of the entire BC lattice hierarchy are obtained in terms of the Riemann theta function.