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IOP Publishing, Inverse Problems, 6(22), p. 2197-2207, 2006

DOI: 10.1088/0266-5611/22/6/017

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Inverse Scattering Transform for the Camassa-Holm equation

Journal article published in 2006 by Adrian Constantin ORCID, Vladimir S. Gerdjikov, Rossen I. Ivanov
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This paper is available in a repository.

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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. ; Comment: 17 pages, LaTeX