On scattering for the cubic defocusing nonlinear Schrödinger equation on the waveguide $\mathbb R^2 \times \mathbb T$

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 $R^{2} \times T$

Xing Cheng
Hohai University, Nanjing, China and Monash University, Australia
Zihua Guo
Monash University, Clayton, Australia
Kailong Yang
University of Sciences and Technology, Beijing, China
Lifeng Zhao
University of Scinece and Technology of China, Hefei, China

$On scattering for the cubic defocusing nonlinear Schrödinger equation on the waveguide $\mathbb R^2 \times \mathbb T$ cover$

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Abstract

In this article, we will show the scattering of the cubic defocusing nonlinear Schrödinger equation on the waveguide $R^{2} \times T$ in $H^{1}$ . We first establish the linear profile decomposition in $H^{1} (R^{2} \times T)$ motivated by the linear profile decomposition of the mass-critical Schrödinger equation in $L^{2} (R^{2})$ . Then by using the solution of the cubic resonant nonlinear Schrödinger system to approximate the nonlinear profile, we can prove scattering in $H^{1}$ by using the concentration-compactness/rigidity method.

Cite this article

Xing Cheng, Zihua Guo, Kailong Yang, Lifeng Zhao, On scattering for the cubic defocusing nonlinear Schrödinger equation on the waveguide $R^{2} \times T$ . Rev. Mat. Iberoam. 36 (2020), no. 4, pp. 985–1011

DOI 10.4171/RMI/1155