Ground states of the two-dimensional dispersion managed nonlinear Schrödinger equation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908062297620480 |
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| author | Choi, Mi-Ran Lee, Young-Ran |
| author_facet | Choi, Mi-Ran Lee, Young-Ran |
| contents | We consider the variational problem with a mass constraint arising from the two-dimensional dispersion managed nonlinear Schrödinger equation with power-law type nonlinearity. We prove a threshold phenomenon with respect to mass for the existence of minimizers for all possible powers of nonlinearities, including at the threshold itself. This threshold is closely related to the best constant for the Gagliardo-Nirenberg-Strichartz type inequality whose extremizers are found as a byproduct. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14686 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ground states of the two-dimensional dispersion managed nonlinear Schrödinger equation Choi, Mi-Ran Lee, Young-Ran Analysis of PDEs 35Q55, 35P30, 49J40 We consider the variational problem with a mass constraint arising from the two-dimensional dispersion managed nonlinear Schrödinger equation with power-law type nonlinearity. We prove a threshold phenomenon with respect to mass for the existence of minimizers for all possible powers of nonlinearities, including at the threshold itself. This threshold is closely related to the best constant for the Gagliardo-Nirenberg-Strichartz type inequality whose extremizers are found as a byproduct. |
| title | Ground states of the two-dimensional dispersion managed nonlinear Schrödinger equation |
| topic | Analysis of PDEs 35Q55, 35P30, 49J40 |
| url | https://arxiv.org/abs/2409.14686 |