Remark on the scattering theory of the nonlinear Schrödinger equation on the cylinders
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929345387298816 |
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| author | Cheng, Xing Zheng, Jiqiang |
| author_facet | Cheng, Xing Zheng, Jiqiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09740 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Remark on the scattering theory of the nonlinear Schrödinger equation on the cylinders Cheng, Xing Zheng, Jiqiang Analysis of PDEs 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. |
| title | Remark on the scattering theory of the nonlinear Schrödinger equation on the cylinders |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.09740 |