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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2512.01506 |
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| _version_ | 1866912740792074240 |
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| author | Aftalion, Amandine Nguyen, Luc |
| author_facet | Aftalion, Amandine Nguyen, Luc |
| contents | Motivated by recent experiments, we study critical points of the Ginzburg-Landau energy in an infinite strip where phase imprinting is applied to half of the domain. We prove that there is a critical width of the cross section below which the soliton solution is a mountain pass solution and the minimizer within the subspace of odd functions. Above the critical width, we find that the mountain pass solution is a vortex with a solitonic behaviour in the infinite direction, called a solitonic vortex. Moreover, depending on the width, we prove that the minimizer in a space with some symmetries can display one or several solitonic vortices. While the problem shares some similarities with the analysis of stability and minimality of the Ginzburg-Landau vortex of degree one in a disk or the whole plane, the change in geometry introduces subtle analytical differences. Extensions to the case of an infinite cylinder in 3D are also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01506 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mountain pass for the Ginzburg-Landau energy in a strip: solitons and solitonic vortices Aftalion, Amandine Nguyen, Luc Analysis of PDEs Motivated by recent experiments, we study critical points of the Ginzburg-Landau energy in an infinite strip where phase imprinting is applied to half of the domain. We prove that there is a critical width of the cross section below which the soliton solution is a mountain pass solution and the minimizer within the subspace of odd functions. Above the critical width, we find that the mountain pass solution is a vortex with a solitonic behaviour in the infinite direction, called a solitonic vortex. Moreover, depending on the width, we prove that the minimizer in a space with some symmetries can display one or several solitonic vortices. While the problem shares some similarities with the analysis of stability and minimality of the Ginzburg-Landau vortex of degree one in a disk or the whole plane, the change in geometry introduces subtle analytical differences. Extensions to the case of an infinite cylinder in 3D are also given. |
| title | Mountain pass for the Ginzburg-Landau energy in a strip: solitons and solitonic vortices |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.01506 |