Inverse scattering transform for the Camassa-Holm equation

Adrian Constantin; Vladimir S. Gerdjikov; Rossen I. Ivanov

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

Inverse scattering transform for the Camassa-Holm equation

Adrian Constantin, Vladimir S. Gerdjikov, Rossen I. Ivanov

Research output: Contribution to journal › Article › peer-review

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 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.

Original language	English
Article number	017
Pages (from-to)	2197-2207
Number of pages	11
Journal	Inverse Problems
Volume	22
Issue number	6
DOIs	https://doi.org/10.1088/0266-5611/22/6/017
Publication status	Published - 1 Dec 2006
Externally published	Yes

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AB - 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 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.

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Inverse scattering transform for the Camassa-Holm equation

Abstract

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