Algebro-geometric solutions for the two-component Camassa-Holm Dym hierarchy

Abstract

This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the two-component Camassa-Holm Dym (CHD2) hierarchy. Our main tools include the polynomial recursive formalism, the hyperelliptic curve with finite number of genus, the Baker-Akhiezer functions, the meromorphic function, the Dubrovin-type equations for auxiliary divisors, and the associated trace formulas. With the help of these tools, the explicit representations of the algebro-geometric solutions are obtained for the entire CHD2 hierarchy.

39 pages. arXiv admin note: substantial text overlap with arXiv:1207.0574, arXiv:1205.6062, arXiv:1305.0122; and with arXiv:nlin/0105021 by other authors