Two-component {CH} system: Inverse Scattering, Peakons and Geometry

Abstract

An inverse scattering transform method corresponding to a Riemann-Hilbert problem is formulated for CH2, the two-component generalization of the Camassa-Holm (CH) equation. As an illustration of the method, the multi - soliton solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data for CH2.

22 pages, 3 figures, draft, please send comments

References in corpus (9)

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• On the absolutely continuous spectrum of generalized indefinite strings
• Real-valued algebro-geometric solutions of the two-component Camassa-Holm hierarchy
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• The conservative Camassa-Holm flow with step-like irregular initial data