Inverse scattering transform for the Camassa–Holm equation
Inverse problems, 2006•iopscience.iop.org
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.
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.
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.
iopscience.iop.org
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