ALGEBRO-GEOMETRIC SOLUTIONS OF THE BOUSSINESQ HIERARCHY

@article{Dickson1999ALGEBROGEOMETRICSO,
  title={ALGEBRO-GEOMETRIC SOLUTIONS OF THE BOUSSINESQ HIERARCHY},
  author={Ronnie Dickson and Fritz Gesztesy and Karl Unterkofler},
  journal={Reviews in Mathematical Physics},
  year={1999},
  volume={11},
  pages={823-879}
}
We continue a recently developed systematic approach to the Bousinesq (Bsq) hierarchy and its algebro-geometric solutions. Our formalism includes a recursive construction of Lax pairs and establishes associated Burchnall–Chaundy curves, Baker–Akhiezer functions and Dubrovin-type equations for analogs of Dirichlet and Neumann divisors. The principal aim of this paper is a detailed theta function representation of all algebro-geometric quasi-periodic solutions and related quantities of the Bsq… 
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  • F. GesztesyH. Holden
  • Mathematics
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2007
TLDR
A detailed treatment of real-valued, smooth and bounded algebro-geometric solutions of the Camassa-Holm (CH) hierarchy is provided and the associated isospectral torus is described.
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