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

Xing Cheng, Zihua Guo, Kailong Yang, Lifeng Zhao

Research output: Contribution to journalArticleResearchpeer-review

2 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 languageEnglish
Pages (from-to)985-1011
Number of pages27
JournalRevista Matematica Iberoamericana
Volume36
Issue number4
DOIs
Publication statusPublished - 10 Jan 2020

Keywords

  • Nonlinear Schrödinger equation
  • Profile decomposition
  • Scattering
  • Waveguide

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