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Zbl 1105.37044
Constantin, Adrian; Gerdjikov, Vladimir S.; Ivanov, Rossen I.
Inverse scattering transform for the Camassa--Holm equation. (English)
[J] Inverse Probl. 22, No. 6, 2197-2207 (2006). ISSN 0266-5611

Summary: 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.

MSC 2000:: *37K15 Integration by inverse spectral and scattering methods
34A55 Inverse problems of ODE
35P25 Scattering theory (PDE)
35Q53 KdV-like equations
35R30 Inverse problems for PDE

Keywords: Riemann-Hilbert problem; reflectionless potentials; analytic solutions; weighted spectral problem

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