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 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.

arXiv comment46 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

References in corpus (4)

• An integrable shallow water equation with peaked solitons
• An Alternative Approach to Algebro-Geometric Solutions of the AKNS Hierarchy
• The Complex Geometry of Weak Piecewise Smooth Solutions of Integrable Nonlinear PDE's of Shallow Water and Dym Type
• Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians