A new proof of long range scattering for critical nonlinear Schrödinger equations

2010/04/05 by Kato, Jun, Pusateri, Fabio · 6 citations
#35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1004.0721

Abstract

We present a new proof of global existence and long range scattering, from small initial data, for the one-dimensional cubic gauge invariant nonlinear Schrödinger equation, and for Hartree equations in dimension n ≥ 2. The proof relies on an analysis in Fourier space, related to the recent works of Germain, Masmoudi and Shatah on space-time resonances. An interesting feature of our approach is that we are able to identify the long range phase correction term through a very natural stationary phase argument.

Cited by

• Modified Scattering for Nonlocal Nonlinear Schrödinger Equations
• Space-time resonances in the spatiotemporal spectrum of nonlinear dispersive waves
• On completeness of modified wave operators for defocusing NLS
• Global solution and asymptotic behavior for the kinetic derivative NLS on \mathbb R
• The cubic NLS on the line with an inverse square potential
• On scattering for NLS: rigidity properties and numerical simulations via the lens transform

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