This item is available under a Creative Commons License for non-commercial use only
Integrable equations with second order Lax pair like KdV and Camassa-Holm (CH) exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants (Schwarz form). These properties for the CH hierarchy are discussed in this ontribution. 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.
R. Ivanov, Conformal and geometric properties of the Camassa-Holm hierarchy, Discrete and Continuous Dynamical Systems 19 (2007) 545 -554