Standing waves of the Anderson-Gross-Pitaevskii equation
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911342607204352 |
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| author | Mackowiak, Samaël |
| author_facet | Mackowiak, Samaël |
| contents | In this paper, we study standing waves for the Anderson-Gross-Pitaevskii equation in dimension 1 and 2. The Anderson-Gross-Pitaevskii equation is a nonlinear Schrödinger equation with a confining potential and a multiplicative spatial white noise. Standing waves are characterized by a profile which is invariant by the dynamic and solves a nonlinear elliptic equation with spatial white noise potential. We construct such solutions via variational methods and obtain some results on their regularity, localization and stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22960 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Standing waves of the Anderson-Gross-Pitaevskii equation Mackowiak, Samaël Analysis of PDEs Mathematical Physics Probability In this paper, we study standing waves for the Anderson-Gross-Pitaevskii equation in dimension 1 and 2. The Anderson-Gross-Pitaevskii equation is a nonlinear Schrödinger equation with a confining potential and a multiplicative spatial white noise. Standing waves are characterized by a profile which is invariant by the dynamic and solves a nonlinear elliptic equation with spatial white noise potential. We construct such solutions via variational methods and obtain some results on their regularity, localization and stability. |
| title | Standing waves of the Anderson-Gross-Pitaevskii equation |
| topic | Analysis of PDEs Mathematical Physics Probability |
| url | https://arxiv.org/abs/2512.22960 |