Inverse Scattering Transform for the Camassa-Holm equation

Details Inverse Scattering Transform for the Camassa-Holm equation Inverse Scattering Transform for the Camassa-Holm equation

2006-03-09

arxiv.org/abs/nlin/0603019v2

Inv. Problems 22 (2006) 2197-2207

Nonlinear Sciences

Exactly Solvable and Integrable Systems

17 pages, LaTeX

Scientific paper

10.1088/0266-5611/22/6/017

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.

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