Zeitschrift für angewandte Mathematik und Physik

, Volume 65, Issue 3, pp 487–520

Algebro-geometric solutions for the Hunter–Saxton hierarchy

Authors

  • Yu Hou
    • School of Mathematical Sciences Institute of Mathematics Key Laboratory of Mathematics for Nonlinear ScienceFudan University
    • School of Mathematical Sciences Institute of Mathematics Key Laboratory of Mathematics for Nonlinear ScienceFudan University
  • Peng Zhao
    • School of Mathematical Sciences Institute of Mathematics Key Laboratory of Mathematics for Nonlinear ScienceFudan University
Article

DOI: 10.1007/s00033-013-0339-8

Cite this article as:
Hou, Y., Fan, E. & Zhao, P. Z. Angew. Math. Phys. (2014) 65: 487. doi:10.1007/s00033-013-0339-8

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.

Mathematics Subject Classification (2000)

35Q5358F07

Keywords

Hunter–Saxton hierarchyAlgebro-geometric initial value problemHyperelliptic curveAlgebro-geometric solutions

Copyright information

© Springer Basel 2013