Abstract
AbstractThe Harry Dym hierarchy is derived with the help of Lenard recursion equations and zero curvature equation. Based on the Lax matrix, an algebraic curve$\mathcal{K}_{n}$of arithmetic genus$n$is introduced, from which the corresponding meromorphic function$\phi$and Dubrovin-type equations are given. Further, the divisor and asymptotic properties of$\phi$are studied. Finally, algebro-geometric solutions for the entire hierarchy are obtained according to above results and the theory of algebraic curve.
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