Standing waves for a Schr\'odinger system with three waves interaction
| Autor: | Forcella, Luigi, Luo, Xiao, Yang, Tao, Yang, Xiaolong |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study standing waves for a system of nonlinear Schr\"odinger 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 synchronised 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 which 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. Comment: 42 pages, submitted paper |
| Databáze: | arXiv |
| Externí odkaz: |
|