Resonant large deviations principle for the beating NLS equation
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917746268176384 |
|---|---|
| author | Grande, Ricardo |
| author_facet | Grande, Ricardo |
| contents | We prove a large deviations principle for the solution to the beating NLS equation on the torus with random initial data supported on two Fourier modes. When these modes have different initial variance, we prove that the resonant energy exchange between them increases the likelihood of extreme wave formation. Our results show that nonlinear focusing mechanisms can lead to tail fattening of the probability measure of the sup-norm of the solution to a nonlinear dispersive equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05791 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Resonant large deviations principle for the beating NLS equation Grande, Ricardo Analysis of PDEs Mathematical Physics 35Q55, 60F10 We prove a large deviations principle for the solution to the beating NLS equation on the torus with random initial data supported on two Fourier modes. When these modes have different initial variance, we prove that the resonant energy exchange between them increases the likelihood of extreme wave formation. Our results show that nonlinear focusing mechanisms can lead to tail fattening of the probability measure of the sup-norm of the solution to a nonlinear dispersive equation. |
| title | Resonant large deviations principle for the beating NLS equation |
| topic | Analysis of PDEs Mathematical Physics 35Q55, 60F10 |
| url | https://arxiv.org/abs/2408.05791 |