Threshold for the existence of scattering states for nonlinear Schrödinger equations without gauge invariance
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915584197787648 |
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| author | Miyazaki, Hayato Sobajima, Motohiro |
| author_facet | Miyazaki, Hayato Sobajima, Motohiro |
| contents | This paper is concerned with a threshold phenomenon for the existence of scattering states for nonlinear Schrödinger equations. The nonlinearity includes a non-oscillatory term of the order lower than the Strauss exponent. We show that no scattering states exist for the equation in a weighted Sobolev space. It is emphasized that our method admits initial data with good properties, such as compactly supported smooth functions. The result indicates that the Strauss exponent acts as a threshold for the power of the nonlinearity that determines whether solutions scatter or not in the weighted space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Threshold for the existence of scattering states for nonlinear Schrödinger equations without gauge invariance Miyazaki, Hayato Sobajima, Motohiro Analysis of PDEs 35Q55, 35P25 This paper is concerned with a threshold phenomenon for the existence of scattering states for nonlinear Schrödinger equations. The nonlinearity includes a non-oscillatory term of the order lower than the Strauss exponent. We show that no scattering states exist for the equation in a weighted Sobolev space. It is emphasized that our method admits initial data with good properties, such as compactly supported smooth functions. The result indicates that the Strauss exponent acts as a threshold for the power of the nonlinearity that determines whether solutions scatter or not in the weighted space. |
| title | Threshold for the existence of scattering states for nonlinear Schrödinger equations without gauge invariance |
| topic | Analysis of PDEs 35Q55, 35P25 |
| url | https://arxiv.org/abs/2503.07983 |