Date: 14 May 2013

Algebro-geometric solutions for the Hunter–Saxton hierarchy

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Abstract

This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the Hunter–Saxton (HS) hierarchy through studying an algebro-geometric initial value problem. 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 HS hierarchy.