Inverse Scattering Transform for the Camassa-Holm equation
Exactly Solvable and Integrable Systems
2007-05-23 v2
Abstract
An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are explicitly constructed in terms of the scattering data. The main difference with respect to the standard Inverse Scattering Transform lies in the fact that we have a weighted spectral problem. We therefore have to develop different asymptotic expansions.
Keywords
Cite
@article{arxiv.nlin/0603019,
title = {Inverse Scattering Transform for the Camassa-Holm equation},
author = {Adrian Constantin and Vladimir S. Gerdjikov and Rossen I. Ivanov},
journal= {arXiv preprint arXiv:nlin/0603019},
year = {2007}
}
Comments
17 pages, LaTeX