On the gap property of a linearized NLS operator
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866912946501713920 |
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| author | Li, Dong Yang, Kai |
| author_facet | Li, Dong Yang, Kai |
| contents | We consider a pair of linear operators corresponding to the linearization around the ground state soliton of the cubic nonlinear Schrödinger equation in dimension three. We introduce a new comparison-based approach and rigorously prove that the interval $(0, 1]$ does not contain any eigenvalues of these operators. Furthermore we show the absence of resonances at the bottom of the essential spectrum. All the obtained results are for the fully non-radial case. The method can be adapted to many other spectral problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_14393 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the gap property of a linearized NLS operator Li, Dong Yang, Kai Analysis of PDEs Mathematical Physics Spectral Theory We consider a pair of linear operators corresponding to the linearization around the ground state soliton of the cubic nonlinear Schrödinger equation in dimension three. We introduce a new comparison-based approach and rigorously prove that the interval $(0, 1]$ does not contain any eigenvalues of these operators. Furthermore we show the absence of resonances at the bottom of the essential spectrum. All the obtained results are for the fully non-radial case. The method can be adapted to many other spectral problems. |
| title | On the gap property of a linearized NLS operator |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2110.14393 |