Algebro-geometric solutions for the Hunter-Saxton hierarchy

作者：Hou Yu^*; Fan Engui; Zhao Peng

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2014, 65(3): 487-520.

DOI：10.1007/s00033-013-0339-8

• Hunter-Saxton hierarchy
• Algebro-geometric initial value problem
• Hyperelliptic curve
• Algebro-geometric solutions

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.

• 出版日期2014-6
• 单位复旦大学