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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2022
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2210.07643 |
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Table des matières:
- 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.