Fractional Gross-Pitaevskii equations in non-Gaussian attractive Bose-Einstein condensates
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909344181780480 |
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| author | Yang, Jinge Yang, Jianfu |
| author_facet | Yang, Jinge Yang, Jianfu |
| contents | In this paper, we investigate normalized solutions of a fractional Gross-Pitaevskii equation, which arises in an attractive Bose-Einstein condensation consisting of $N$ bosons moving by Lévy flights. We prove that there exists a positive constant $N^*$, such that if $0<N<N^*$ and the Lévy index $α$ closed to $2$, the fractional Gross-Pitaevskii equation admits a local minimal normalized solution $u_α$ and a mountain pass solution $v_α$, but there does not exist positive local minimal solution if $N>N^*$ and $α$ closed to $2$. We also study the asymptotic behavior of $u_α$ and $v_α$ as $α\to 2_-$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07510 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional Gross-Pitaevskii equations in non-Gaussian attractive Bose-Einstein condensates Yang, Jinge Yang, Jianfu Analysis of PDEs In this paper, we investigate normalized solutions of a fractional Gross-Pitaevskii equation, which arises in an attractive Bose-Einstein condensation consisting of $N$ bosons moving by Lévy flights. We prove that there exists a positive constant $N^*$, such that if $0<N<N^*$ and the Lévy index $α$ closed to $2$, the fractional Gross-Pitaevskii equation admits a local minimal normalized solution $u_α$ and a mountain pass solution $v_α$, but there does not exist positive local minimal solution if $N>N^*$ and $α$ closed to $2$. We also study the asymptotic behavior of $u_α$ and $v_α$ as $α\to 2_-$. |
| title | Fractional Gross-Pitaevskii equations in non-Gaussian attractive Bose-Einstein condensates |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.07510 |