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This article is available for purchase or by subscription. See below.
Abstract
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We study the asymptotic behavior of a quadratic NLS equation with small,
time-dependent potential and small spatially localized initial data. We prove global
existence and scattering of solutions. The two main ingredients of the proof are the
space-time resonance method and the boundedness of wave operators for the linear
Schrödinger equation with potential.
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Keywords
space-time resonances, Schrödinger equation
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Mathematical Subject Classification 2010
Primary: 35Q55
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Milestones
Received: 25 April 2018
Revised: 2 April 2020
Accepted: 6 May 2020
Published: 10 November 2021
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