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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2210.07643 |
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| _version_ | 1866910129571495936 |
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| author | Forcella, Luigi Luo, Xiao Yang, Tao Yang, Xiaolong |
| author_facet | Forcella, Luigi Luo, Xiao Yang, Tao Yang, Xiaolong |
| contents | We study standing waves for a system of nonlinear Schrödinger equations with three waves interaction arising as a model for the Raman amplification in a plasma. We consider the mass-critical and mass-supercritical regimes, and we prove existence of ground states along with a synchronized mass collapse behavior. In addition, we show that the set of ground states is stable under the associated Cauchy flow. Furthermore, in the mass-supercritical setting we construct an excited state that corresponds to a strongly unstable standing wave. Moreover, a semi-trivial limiting behavior of the excited state is drawn accurately. Finally, by a refined control of the excited state's energy, we give sufficient conditions to prove global existence or blow-up of solutions to the corresponding Cauchy problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_07643 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Standing waves for a Schrödinger system with three waves interaction Forcella, Luigi Luo, Xiao Yang, Tao Yang, Xiaolong Analysis of PDEs We study standing waves for a system of nonlinear Schrödinger equations with three waves interaction arising as a model for the Raman amplification in a plasma. We consider the mass-critical and mass-supercritical regimes, and we prove existence of ground states along with a synchronized mass collapse behavior. In addition, we show that the set of ground states is stable under the associated Cauchy flow. Furthermore, in the mass-supercritical setting we construct an excited state that corresponds to a strongly unstable standing wave. Moreover, a semi-trivial limiting behavior of the excited state is drawn accurately. Finally, by a refined control of the excited state's energy, we give sufficient conditions to prove global existence or blow-up of solutions to the corresponding Cauchy problem. |
| title | Standing waves for a Schrödinger system with three waves interaction |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2210.07643 |