The algebro-geometric solutions for Hunter-Saxton hierarchy
arXiv:1207.0574
Abstract
This paper is dedicated to provide theta function representation of algebro-geometric solutions and related crucial quantities for the Hunter-Saxton (HS) hierarchy through studying a algebro-geometric initial value problem. Our main tools include the polynomial recursive formalism to derive the HS hierarchy, 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 Baker-Ahhiezer functions, the meromorphic function, and the algebro-geometric solutions are obtained for the entire HS hierarchy.
arXiv comment50 pages. arXiv admin note: substantial text overlap with arXiv:1205.6062
References in corpus (5)
- An integrable shallow water equation with peaked solitons
- An Alternative Approach to Algebro-Geometric Solutions of the AKNS Hierarchy
- On a Whitham-Type Equation
- Contact Equivalence of the Generalized Hunter - Saxton Equation and the Euler - Poisson Equation
- The algebro-geometric solutions for the modified Camassa-Holm hierarchy