A new proof of a Liouville theorem for the one dimensional Gross-Pitaevskii equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915372449398784 |
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| author | Kowalczyk, Michał Martel, Yvan |
| author_facet | Kowalczyk, Michał Martel, Yvan |
| contents | The asymptotic stability of the black and dark solitons of the one-dimensional Gross-Pitaevskii equation was proved by Béthuel, Gravejat and Smets (Ann. Sci. Éc. Norm. Supér. 48 (2015)) and Gravejat and Smets (Proc. Lond. Math. Soc. 111 (2015)), using a rigidity property in the vicinity of solitons. We provide an alternate proof of the Liouville theorems in the above articles using a factorization identity for the linearized operator which trivializes the spectral analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03966 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new proof of a Liouville theorem for the one dimensional Gross-Pitaevskii equation Kowalczyk, Michał Martel, Yvan Analysis of PDEs The asymptotic stability of the black and dark solitons of the one-dimensional Gross-Pitaevskii equation was proved by Béthuel, Gravejat and Smets (Ann. Sci. Éc. Norm. Supér. 48 (2015)) and Gravejat and Smets (Proc. Lond. Math. Soc. 111 (2015)), using a rigidity property in the vicinity of solitons. We provide an alternate proof of the Liouville theorems in the above articles using a factorization identity for the linearized operator which trivializes the spectral analysis. |
| title | A new proof of a Liouville theorem for the one dimensional Gross-Pitaevskii equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.03966 |