Hodograph transformations for a Camassa- Holm hierarchy in 2+1 dimensions
arXiv:nlin/0412019 · doi:10.1088/0305-4470/38/6/008
Abstract
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..
14 pages. To appear in J. Phys. A: Math. And Gen