Action of a scattering map on weighted Sobolev spaces in the plane

preprint2016arXivOpen access

We consider a scattering map that arises in the $\bar \partial$ -approach to the scattering theory for the Davey-Stewartson II equation and show that the map is an invertible map between certain weighted $L^2$ Sobolev spaces.

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Action of a scattering map on weighted Sobolev spaces in the plane

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