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Variational derivation of the Camassa-Holm shallow water equation with non-zero vorticity
Conformal and Geometric Properties of the Camassa-Holm Hierarchy
| 1. | School of Mathematics, Trinity College Dublin, Dublin 2, Ireland |
The squared eigenfunctions of the spectral problem, associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform (IST) for the Camassa-Holm hierarchy as a Generalised Fourier Transform (GFT). Using GFT we describe explicitly some members of the CH hierarchy, including integrable deformations for the CH equation. Also we show that solutions of some 2+1-dimensional generalizations of CH can be constructed via the IST for the CH hierarchy.
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