Algebro-geometric solutions of the coupled modified Korteweg-de Vries hierarchy

Based on the stationary zero-curvature equation and the Lenard recursion equations, we derive the coupled modified Korteweg-de Vries (cmKdV) hierarchy associated with a 3 x 3 matrix spectral problem. Resorting to. the Baker-Akhiezer function and the characteristic polynomial of Lax matrix for the cmKdV hierarchy, we introduce a trigonal curve with three infinite points and two algebraic functions carrying the data of the divisor. The asymptotic properties of the Baker-Akhiezer function and the two algebraic functions are studied near three infinite points on the trigonal curve. Algebro-geometric solutions of the cmKdV hierarchy are obtained in terms of the Riemann theta function. (C) 2014 Elsevier Inc. All rights reserved.