Global bounds for the cubic nonlinear Schr\"odinger equation (NLS) in one space dimension

Mihaela Ifrim; Daniel Tataru

Global bounds for the cubic nonlinear Schr\"odinger equation (NLS) in one space dimension

Analysis of PDEs 2014-10-14 v2

Authors: Mihaela Ifrim , Daniel Tataru

Abstract

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.

Keywords

cubic nonlinear Schrödinger equation global bounds small data problem modified scattering asymptotic completeness one space dimension H^{0,1}

Cite

@article{arxiv.1404.7581,
  title  = {Global bounds for the cubic nonlinear Schr\"odinger equation (NLS) in one space dimension},
  author = {Mihaela Ifrim and Daniel Tataru},
  journal= {arXiv preprint arXiv:1404.7581},
  year   = {2014}
}

Comments

15 pages. We fixed the proof of Lemma 2.4

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