Bibliographic Details
| Title: |
Threshold for the existence of scattering states for nonlinear Schr\'odinger equations without gauge invariance |
| Authors: |
Miyazaki, Hayato, Sobajima, Motohiro |
| Publication Year: |
2025 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Analysis of PDEs, 35Q55, 35P25 |
| More Details: |
This paper is concerned with a threshold phenomenon for the existence of scattering states for nonlinear Schr\"odinger 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.
Comment: 10 pages |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2503.07983 |
| Accession Number: |
edsarx.2503.07983 |
| Database: |
arXiv |
