Trapping by repulsion: the NLS with a delta-prime
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908431620767744 |
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| author | Adami, Riccardo Boni, Filippo Gallone, Matteo |
| author_facet | Adami, Riccardo Boni, Filippo Gallone, Matteo |
| contents | We establish the existence and provide explicit expressions for the stationary states of the one-dimensional Schrödinger equation with a repulsive delta-prime potential and a focusing nonlinearity of power type. Furthermore, we prove that, if the nonlinearity is subcritical, then ground states exist for any strength of the delta-prime interaction and for every positive value of the mass.
This result supplies an example of ground states arising from a repulsive potential, a counterintuitive phenomenon explained by the emergence of an additional dimension in the energy space, induced by the delta-prime interaction. This new dimension contains states of lower energy and is thus responsible for the existence of nonlinear ground states that do not originate from linear eigenfunctions.
The explicit form of the ground states is derived by addressing the ancillary problem of minimizing the action functional on the Nehari manifold. We solve such problem in the subcritical, critical, and supercritical regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02330 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trapping by repulsion: the NLS with a delta-prime Adami, Riccardo Boni, Filippo Gallone, Matteo Analysis of PDEs Mathematical Physics 35Q40, 35Q55, 49J40 We establish the existence and provide explicit expressions for the stationary states of the one-dimensional Schrödinger equation with a repulsive delta-prime potential and a focusing nonlinearity of power type. Furthermore, we prove that, if the nonlinearity is subcritical, then ground states exist for any strength of the delta-prime interaction and for every positive value of the mass. This result supplies an example of ground states arising from a repulsive potential, a counterintuitive phenomenon explained by the emergence of an additional dimension in the energy space, induced by the delta-prime interaction. This new dimension contains states of lower energy and is thus responsible for the existence of nonlinear ground states that do not originate from linear eigenfunctions. The explicit form of the ground states is derived by addressing the ancillary problem of minimizing the action functional on the Nehari manifold. We solve such problem in the subcritical, critical, and supercritical regimes. |
| title | Trapping by repulsion: the NLS with a delta-prime |
| topic | Analysis of PDEs Mathematical Physics 35Q40, 35Q55, 49J40 |
| url | https://arxiv.org/abs/2507.02330 |