2013/05/13 by Yu Hou, Engui Fan, Peng Zhao
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Finite set #Function (biology) #Hierarchy #Homotopy and Cohomology in Algebraic Topology #Meromorphic function #Nonlinear Waves and Solitons #Polynomial #TRACE (psycholinguistics) #nlin.SI
paper · pdf · doi:10.1007/s00033-013-0339-8
46 pages. accepted for publication J Nonl Math Phys, 2014. arXiv admin note: substantial text overlap with arXiv:1406.6153, arXiv:1207.0574, arXiv:1205.6062; and with arXiv:nlin/0105021 by other authors
openalex publication_date 2013/05/13 · arxiv created 2014/09/14 · arxiv updated 2015/06/22 · openalex created_date 2017/10/20 · openalex updated_date 2026/08/05
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 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 HS2 hierarchy.