Finite-band solutions of the coupled dispersionless hierarchy

Abstract

The coupled dispersionless hierarchy is derived with the help of the zero curvature equation. Based on the Lax matrix, we introduce an algebraic curve of arithmetic genus n, from which we establish the corresponding meromorphic function ϕ, the Baker–Akhiezer function , and Dubrovin-type equations. The straightening out of all the flows is given under the Abel–Jacobi coordinates. Using the asymptotic properties of ϕ and , we obtain the explicit theta function representations of the meromorphic function ϕ, the Baker–Akhiezer function and of solutions for the whole hierarchy.