S I ] 1 3 Ju l 2 00 7 Generalised Fourier transform for the Camassa-Holm hierarchy

@inproceedings{Constantin2008SI,
title={S I ] 1 3 Ju l 2 00 7 Generalised Fourier transform for the Camassa-Holm hierarchy},
author={Adrian Constantin and V. S. Gerdjikov and Rossen I. Ivanov},
year={2008}
}

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 for the Camassa-Holm hierarchy as a Generalised Fourier transform. The main result of this work is the derivation of the completeness relation for the squared solutions of the Camassa-Holm spectral problem. We show that all the fundamental properties of the Camassa-Holm equation such as the integrals of… CONTINUE READING