Abstract In the article, we prove the large data scattering for two models, i.e. the defocusing quintic nonlinear Schrodinger equation on R 2 × T and the defocusing cubic nonlinear Schrodinger equation on R 3 × T . Both of the two equations are mass supercritical and energy critical. The main ingredients of the proofs contain global Stricharz estimate, profile decomposition and energy induction method. This paper is the second project of our series work (two papers, together with [31] ) on large data scattering for the defocusing critical NLS with integer index nonlinearity on low dimensional waveguides. At this point, this category of problems are almost solved except for two remaining resonant system conjectures and the quintic NLS problem on R × T .

中文翻译：

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关于散焦非线性薛定谔方程在波导 Rm×T 上的散射（当 m = 2,3 时）

摘要 本文证明了R 2 × T 上的离焦五次非线性薛定谔方程和R 3 × T 上的离焦三次非线性薛定谔方程两种模型的大数据散射。这两个方程都是质量超临界和能量临界的。证明的主要内容包括全局 Stricharz 估计、剖面分解和能量归纳方法。这篇论文是我们系列工作的第二个项目（两篇论文，连同 [31]），关于低维波导上具有整数折射率非线性的散焦临界 NLS 的大数据散射。至此，除了剩下的两个共振系统猜想和 R × T 上的五次 NLS 问题外，这一类问题几乎都解决了。