Algebro-geometric solutions for the two-component Hunter-Saxton hierarchy

Abstract

This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the two-component Hunter-Saxton (HS2) hierarchy through 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 HS2 hierarchy.

Keywords:

• Hyperelliptic curve
• Baker-Akhiezer function
• Algebro-geometric solutions
• Trace formulas

2000 Mathematics Subject Classification:

• 35Q53
• 58F07
• 53C35