Energy scattering theory for NLS with  potentials in dimension one

ZHANG Jun-Yong

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Energy scattering theory for NLS with potentials in dimension one

ZHANG Jun-Yong *

Department of Mathematics, Beijing Institute of Technology, Beijing, 100081

*Correspondence author

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Funding: RFDP （No.20121101120044）

Opened online:13 May 2016

Accepted by: none

Citation: ZHANG Jun-Yong.Energy scattering theory for NLS with potentials in dimension one[OL]. [13 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4687700

This paper is devoted to study the scattering theory for the defocusing nonlinear Schr"odinger equations withpotentials $ipartial_tu+Delta u-V(x)u=|u|^{p-1}u$ in dimensionone. The new ingredients are the interaction Morawetz-typeinequalities. One can utilize such estimate to show the scattering holdsin the energy space $H^1(mathbb{R})$.

Keywords:Nonlinear Schr¨odinger equations; global well-posedness; scattering

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