On the ground state of the nonlinear Schr{ö}dinger equation: asymptotic behavior at the endpoint powers
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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_ | 1866911505485660160 |
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| author | Carles, Rémi Chauleur, Quentin Ferriere, Guillaume Pelinovsky, Dmitry |
| author_facet | Carles, Rémi Chauleur, Quentin Ferriere, Guillaume Pelinovsky, Dmitry |
| contents | We consider the ground states of the nonlinear Schr{ö}dinger equation, which stand for radially symmetric and exponentially decaying solutions on the full space. We investigate their behaviors at both endpoint powers of the nonlinearity, up to some rescaling to infer non-trivial limits. One case corresponds to the limit towards a Gaussian function called Gausson, which is the ground state of the stationary logarithmic Schr{ö}dinger equation. The other case, for dimension at least three, corresponds to the limit towards the Aubin-Talenti algebraic soliton. We prove strong convergence with explicit bounds for both cases, and provide detailed asymptotics. These theoretical results are illustrated with numerical approximations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10690 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the ground state of the nonlinear Schr{ö}dinger equation: asymptotic behavior at the endpoint powers Carles, Rémi Chauleur, Quentin Ferriere, Guillaume Pelinovsky, Dmitry Analysis of PDEs Mathematical Physics We consider the ground states of the nonlinear Schr{ö}dinger equation, which stand for radially symmetric and exponentially decaying solutions on the full space. We investigate their behaviors at both endpoint powers of the nonlinearity, up to some rescaling to infer non-trivial limits. One case corresponds to the limit towards a Gaussian function called Gausson, which is the ground state of the stationary logarithmic Schr{ö}dinger equation. The other case, for dimension at least three, corresponds to the limit towards the Aubin-Talenti algebraic soliton. We prove strong convergence with explicit bounds for both cases, and provide detailed asymptotics. These theoretical results are illustrated with numerical approximations. |
| title | On the ground state of the nonlinear Schr{ö}dinger equation: asymptotic behavior at the endpoint powers |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2512.10690 |