On the radius of spatial analyticity for defocusing nonlinear Schrödinger equations

Jaeseop Ahn; Jimyeong Kim; Ihyeok Seo

doi:10.3934/dcds.2020016

Article Contents

2020, Volume 40, Issue 1: 423-439. Doi: 10.3934/dcds.2020016

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On the radius of spatial analyticity for defocusing nonlinear Schrödinger equations

Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea

^* Corresponding author: Ihyeok Seo
^* Corresponding author: Ihyeok Seo

Received: January 31, 2019

Revised: June 30, 2019

Published: October 2019

This research was supported by NRF-2019R1F1A1061316

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Abstract

In this paper we study spatial analyticity of solutions to the defocusing nonlinear Schrödinger equations $ iu_t + \Delta u = |u|^{p-1}u $, given initial data which is analytic with fixed radius. It is shown that the uniform radius of spatial analyticity of solutions at later time $ t $ cannot decay faster than $ 1/|t| $ as $ |t|\rightarrow\infty $. This extends the previous work of Tesfahun [19] for the cubic case $ p = 3 $ to the cases where $ p $ is any odd integer greater than $ 3 $.

Keywords:

Spatial analyticity,
nonlinear Schrödinger equations.

Mathematics Subject Classification: Primary: 32D15; Secondary: 35Q55.

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References

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