Global bounds for the cubic nonlinear Schrödinger equation (NLS) in one space dimension

2014/04/30 by Ifrim, Mihaela, Tataru, Daniel · 4 citations
#35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1404.7581

Abstract

This article is concerned with the small data problem for the cubic nonlinear Schrödinger 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.

Cited by

• Modified Scattering for Nonlocal Nonlinear Schrödinger Equations
• Modified Scattering and Asymptotic Completeness for the Derivative Nonlinear Schrödinger equation
• Global solution and asymptotic behavior for the kinetic derivative NLS on \mathbb R
• The cubic NLS on the line with an inverse square potential

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