On scattering for the cubic defocusing nonlinear Schrödinger equation on the waveguide R2 × T

Xing Cheng; Zihua Guo; Kailong Yang; Lifeng Zhao

doi:10.4171/RMI/1155

On scattering for the cubic defocusing nonlinear Schrödinger equation on the waveguide R² × T

Xing Cheng, Zihua Guo, Kailong Yang, Lifeng Zhao

School of Mathematics

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

4 Citations (Scopus)

Abstract

In this article, we will show the scattering of the cubic defocusing nonlinear Schrödinger equation on the waveguide R² ×T in H¹. We first establish the linear profile decomposition in H¹(R² ×T) motivated by the linear profile decomposition of the mass-critical Schrödinger equation in L²(R²). Then by using the solution of the cubic resonant nonlinear Schrödinger system to approximate the nonlinear profile, we can prove scattering in H¹ by using the concentration-compactness/rigidity method.

Original language	English
Pages (from-to)	985-1011
Number of pages	27
Journal	Revista Matematica Iberoamericana
Volume	36
Issue number	4
DOIs	https://doi.org/10.4171/RMI/1155
Publication status	Published - 10 Jan 2020

Keywords

Nonlinear Schrödinger equation
Profile decomposition
Scattering
Waveguide

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10.4171/RMI/1155

Cite this

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title = "On scattering for the cubic defocusing nonlinear Schr{\"o}dinger equation on the waveguide R2 × T",

abstract = "In this article, we will show the scattering of the cubic defocusing nonlinear Schr{\"o}dinger equation on the waveguide R2 ×T in H1. We first establish the linear profile decomposition in H1(R2 ×T) motivated by the linear profile decomposition of the mass-critical Schr{\"o}dinger equation in L2(R2). Then by using the solution of the cubic resonant nonlinear Schr{\"o}dinger system to approximate the nonlinear profile, we can prove scattering in H1 by using the concentration-compactness/rigidity method.",

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AU - Guo, Zihua

AU - Yang, Kailong

AU - Zhao, Lifeng

PY - 2020/1/10

Y1 - 2020/1/10

N2 - In this article, we will show the scattering of the cubic defocusing nonlinear Schrödinger equation on the waveguide R2 ×T in H1. We first establish the linear profile decomposition in H1(R2 ×T) motivated by the linear profile decomposition of the mass-critical Schrödinger equation in L2(R2). Then by using the solution of the cubic resonant nonlinear Schrödinger system to approximate the nonlinear profile, we can prove scattering in H1 by using the concentration-compactness/rigidity method.

AB - In this article, we will show the scattering of the cubic defocusing nonlinear Schrödinger equation on the waveguide R2 ×T in H1. We first establish the linear profile decomposition in H1(R2 ×T) motivated by the linear profile decomposition of the mass-critical Schrödinger equation in L2(R2). Then by using the solution of the cubic resonant nonlinear Schrödinger system to approximate the nonlinear profile, we can prove scattering in H1 by using the concentration-compactness/rigidity method.

KW - Nonlinear Schrödinger equation

KW - Profile decomposition

KW - Scattering

KW - Waveguide

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