On scattering for the cubic defocusing nonlinear Schrödinger equation on the waveguide

  • 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 in . We first establish the linear profile decomposition in motivated by the linear profile decomposition of the mass-critical Schrödinger equation in . Then by using the solution of the cubic resonant nonlinear Schrödinger system to approximate the nonlinear profile, we can prove scattering in 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 . Rev. Mat. Iberoam. 36 (2020), no. 4, pp. 985–1011

DOI 10.4171/RMI/1155