Remark on the scattering theory of the nonlinear Schrödinger equation on the cylinders

Xing Cheng; Jiqiang Zheng

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arXiv · 2405.09740

Remark on the scattering theory of the nonlinear Schrödinger equation on the cylinders

Xing Cheng·Jiqiang Zheng

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Abstract

In this article, we consider the nonlinear Schrödinger equation on the cylinder $\mathbb{R}^d\times \mathbb{T}$. In the long range case, we show there is no linear scattering state of the nonlinear Schrödinger equation on $\mathbb{R}^d \times \mathbb{T}$. In the short range case, we show the decay and scattering of solutions of the nonlinear Schrödinger equation on $\mathbb{R}^d \times \mathbb{T}$ for small data.

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Xing Cheng, Jiqiang Zheng. 2024-05-16. Remark on the scattering theory of the nonlinear Schrödinger equation on the cylinders. https://arxiv.org/abs/2405.09740

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