Inverse scattering transform for the Camassa–Holm equation
Adrian ConstantinSchool of Mathematics, Trinity College Dublin, Dublin 2, Republic of IrelandVladimir S GerdjikovInstitute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigradsko Chaussee, 1784 Sofia, BulgariaRossen I IvanovSchool of Mathematics, Trinity College Dublin, Dublin 2, Republic of Ireland
2006en
ABI
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.
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