Asymptotics for the fourth-order nonlinear Schrödinger equation in the critical case

Nakao Hayashi; Jesus A. Mendez-Navarro; Pavel I. Naumkin

doi:10.1016/j.jde.2016.07.026

Asymptotics for the fourth-order nonlinear Schrödinger equation in the critical case

Nakao Hayashi, Jesus A. Mendez-Navarro, Pavel I. Naumkin

Research output: Contribution to journal › Article

6 Citations (Scopus)

Abstract

We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation{i∂_tu−14∂x4u=λ|u|⁴u, (t,x)∈R⁺×R,u(0,x)=u₀(x), x∈R. We prove the large time asymptotic behavior of solutions with a logarithmic correction under the conditions ∫u₀(x)dx≠0, λ>0.

Original language	English
Pages (from-to)	5144-5179
Number of pages	36
Journal	Journal of Differential Equations
Volume	261
Issue number	9
DOIs	https://doi.org/10.1016/j.jde.2016.07.026
Publication status	Published - 2016 Nov 5
Externally published	Yes

Keywords

Fourth-order nonlinear Schrödinger equation
Large time asymptotics

ASJC Scopus subject areas

Analysis
Applied Mathematics

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Hayashi, N., Mendez-Navarro, J. A., & Naumkin, P. I. (2016). Asymptotics for the fourth-order nonlinear Schrödinger equation in the critical case. Journal of Differential Equations, 261(9), 5144-5179. https://doi.org/10.1016/j.jde.2016.07.026

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AU - Hayashi, Nakao

AU - Mendez-Navarro, Jesus A.

AU - Naumkin, Pavel I.

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Y1 - 2016/11/5

N2 - We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation{i∂tu−14∂x4u=λ|u|4u, (t,x)∈R+×R,u(0,x)=u0(x), x∈R. We prove the large time asymptotic behavior of solutions with a logarithmic correction under the conditions ∫u0(x)dx≠0, λ>0.

AB - We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation{i∂tu−14∂x4u=λ|u|4u, (t,x)∈R+×R,u(0,x)=u0(x), x∈R. We prove the large time asymptotic behavior of solutions with a logarithmic correction under the conditions ∫u0(x)dx≠0, λ>0.

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KW - Large time asymptotics

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