Propagation of coherent states in the logarithmic Schrodinger equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915306855727104 |
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| author | Carles, Rémi Dong, Fangyuan |
| author_facet | Carles, Rémi Dong, Fangyuan |
| contents | We consider the logarithmic Schr{ö}dinger equation in a semiclassical scaling, in the presence of a smooth, at most quadratic, external potential. For initial data under the form of a single coherent state, we identify the notion of criticality as far as the nonlinear coupling constant is concerned, in the semiclassical limit. In the critical case, we prove a general error estimate, and improve it in the case of initial Gaussian profiles. In this critical case, when the initial datum is the sum of two Gaussian coherent states with different centers in phase space, we prove a nonlinear superposition principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16809 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Propagation of coherent states in the logarithmic Schrodinger equation Carles, Rémi Dong, Fangyuan Analysis of PDEs We consider the logarithmic Schr{ö}dinger equation in a semiclassical scaling, in the presence of a smooth, at most quadratic, external potential. For initial data under the form of a single coherent state, we identify the notion of criticality as far as the nonlinear coupling constant is concerned, in the semiclassical limit. In the critical case, we prove a general error estimate, and improve it in the case of initial Gaussian profiles. In this critical case, when the initial datum is the sum of two Gaussian coherent states with different centers in phase space, we prove a nonlinear superposition principle. |
| title | Propagation of coherent states in the logarithmic Schrodinger equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.16809 |