Hodograph transformations for a Camassa- Holm hierarchy in 2+1 dimensions

Details Hodograph transformations for a Camassa- Holm hierarchy in 2+1 dimensions Hodograph transformations for a Camassa- Holm hierarchy in 2+1 dimensions

2004-12-07

arxiv.org/abs/nlin/0412019v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages. To appear in J. Phys. A: Math. And Gen

Scientific paper

10.1088/0305-4470/38/6/008

A generalization of the negative Camassa-Holm hierarchy to 2+1 dimensions is presented under the name CHH(2+1). Several hodograph transformations are applied in order to transform the hierarchy into a system of coupled CBS (Calogero-Bogoyavlenskii-Schiff) equations in 2+1 dimensions that pass the Painleve test. A non-isospectral Lax pair for CHH(2+1) is obtained through the above mentioned relationship with the CBS spectral problem..

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