Singular sector of the Burgers-Hopf hierarchy and deformations of hyperelliptic curves

Details Singular sector of the Burgers-Hopf hierarchy and deformations of hyperelliptic curves Singular sector of the Burgers-Hopf hierarchy and deformations of hyperelliptic curves

2002-05-06

arxiv.org/abs/nlin/0205012v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, AMSLaTeX, Corrected some minor errors, the final version has appeared in J. Phys. A: Gen. 35 (2002) L489-L500

Scientific paper

10.1088/0305-4470/35/31/104

We discuss the structure of shock singularities of the Burgers-Hopf hierarchy. It is shown that the set of singular solutions defines a stratification of the affine space of the flow parameters in the hierarchy. The stratification is associated with the Birkhoff decomposition of the Grassmannian given by the set of linear spaces spanned by the hierarchy. We then construct integrable hierarchy on each stratum and demonstrate that it describes a deformation of a hyperelliptic curve parametrizing the stratum. The hierarchy is called the hidden Burgers-Hopf hierarchy, and we found the Riemann invarint form and the hodograph solution.

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