Propagation of radius of analyticity for solutions to a fourth-order nonlinear Schrödinger equation

Tegegne Getachew; Birilew Belayneh; Achenef Tesfahun

doi:10.1002/mma.10309

Propagation of radius of analyticity for solutions to a fourth-order nonlinear Schrödinger equation

Tegegne Getachew, Birilew Belayneh, Achenef Tesfahun

School of Sciences and Humanities

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that the uniform radius of spatial analyticity (Formula presented.) of solution at time (Formula presented.) to the one-dimensional fourth-order nonlinear Schrödinger equation (Formula presented.) cannot decay faster than (Formula presented.) for large (Formula presented.), given that the initial data are analytic with fixed radius (Formula presented.). The main ingredients in the proof are a modified Gevrey space, a method of approximate conservation law, and a Strichartz estimate for free wave associated with the equation.

Original language	English
Journal	Mathematical Methods in the Applied Sciences
DOIs	https://doi.org/10.1002/mma.10309
Publication status	Accepted/In press - 2024

Keywords

fourth-order NLS
lower bound
modified Gevrey spaces
radius of analyticity

ASJC Scopus subject areas

General Mathematics
General Engineering

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10.1002/mma.10309

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title = "Propagation of radius of analyticity for solutions to a fourth-order nonlinear Schr{\"o}dinger equation",

abstract = "We prove that the uniform radius of spatial analyticity (Formula presented.) of solution at time (Formula presented.) to the one-dimensional fourth-order nonlinear Schr{\"o}dinger equation (Formula presented.) cannot decay faster than (Formula presented.) for large (Formula presented.), given that the initial data are analytic with fixed radius (Formula presented.). The main ingredients in the proof are a modified Gevrey space, a method of approximate conservation law, and a Strichartz estimate for free wave associated with the equation.",

keywords = "fourth-order NLS, lower bound, modified Gevrey spaces, radius of analyticity",

author = "Tegegne Getachew and Birilew Belayneh and Achenef Tesfahun",

note = "Publisher Copyright: {\textcopyright} 2024 John Wiley & Sons Ltd.",

year = "2024",

doi = "10.1002/mma.10309",

language = "English",

journal = "Mathematical Methods in the Applied Sciences",

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TY - JOUR

T1 - Propagation of radius of analyticity for solutions to a fourth-order nonlinear Schrödinger equation

AU - Getachew, Tegegne

AU - Belayneh, Birilew

AU - Tesfahun, Achenef

PY - 2024

Y1 - 2024

N2 - We prove that the uniform radius of spatial analyticity (Formula presented.) of solution at time (Formula presented.) to the one-dimensional fourth-order nonlinear Schrödinger equation (Formula presented.) cannot decay faster than (Formula presented.) for large (Formula presented.), given that the initial data are analytic with fixed radius (Formula presented.). The main ingredients in the proof are a modified Gevrey space, a method of approximate conservation law, and a Strichartz estimate for free wave associated with the equation.

AB - We prove that the uniform radius of spatial analyticity (Formula presented.) of solution at time (Formula presented.) to the one-dimensional fourth-order nonlinear Schrödinger equation (Formula presented.) cannot decay faster than (Formula presented.) for large (Formula presented.), given that the initial data are analytic with fixed radius (Formula presented.). The main ingredients in the proof are a modified Gevrey space, a method of approximate conservation law, and a Strichartz estimate for free wave associated with the equation.

KW - fourth-order NLS

KW - lower bound

KW - modified Gevrey spaces

KW - radius of analyticity

UR - http://www.scopus.com/inward/record.url?scp=85197454271&partnerID=8YFLogxK

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DO - 10.1002/mma.10309

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SN - 0170-4214

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

ER -

Propagation of radius of analyticity for solutions to a fourth-order nonlinear Schrödinger equation

Abstract

Keywords

ASJC Scopus subject areas

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