Mihaela Ifrim, Daniel Tataru
Published 2014-04-30, updated 2014-10-12Version 2
This article is concerned with the small data problem for the cubic nonlinear Schr\"odinger equation (NLS) in one space dimension, and short range modifications of it. We provide a new, simpler approach in order to prove that global solutions exist for data which is small in $H^{0,1}$. In the same setting we also discuss the related problems of obtaining a modified scattering expansion for the solution, as well as asymptotic completeness.
Comments: 15 pages. We fixed the proof of Lemma 2.4
Modified scattering for the cubic nonlinear Schrödinger equation with long-range potentials in one space dimension
Almost sure well-posedness of the cubic nonlinear Schrödinger equation below L^2(T)
The cubic nonlinear Schrödinger equation in two dimensions with radial data
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