Abstract
We consider the scattering problem for the nonlinear Schrödinger equation in 1+1 dimensions:
where ∂ = ∂/∂x,λ∈R∖{0},μ∈R,p>3. We show that modified wave operators for (*) exist on a dense set of a neighborhood of zero in the Lebesgue spaceL 2(R) or in the Sobolev spaceH 1(R)., The modified wave operators are introduced in order to control the long range nonlinearity λ|u|2 u.
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Communicated by J. Fröhlich
Laboratoire associé au Centre National de la Recherche Scientifique
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Ozawa, T. Long range scattering for nonlinear Schrödinger equations in one space dimension. Commun.Math. Phys. 139, 479–493 (1991). https://doi.org/10.1007/BF02101876
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DOI: https://doi.org/10.1007/BF02101876