Long time dynamics of space periodic water waves
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912789936734208 |
|---|---|
| author | Berti, Massimiliano |
| author_facet | Berti, Massimiliano |
| contents | We review recent advances regarding the long-time dynamics of space-periodic water waves, focusing on 1) bifurcation of quasi-periodic solutions, both standing and traveling; 2) long-time well-posedness results; 3) modulational instability of Stokes waves. These results rely on unconventional approaches to KAM and Birkhoff normal form theories for Hamiltonian quasi-linear PDEs and symplectic Kato perturbation theory for separated eigenvalues of reversible and Hamiltonian operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22115 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long time dynamics of space periodic water waves Berti, Massimiliano Analysis of PDEs 76B15, 37K55, 35R35, 35C07, 35P05, 37J40 We review recent advances regarding the long-time dynamics of space-periodic water waves, focusing on 1) bifurcation of quasi-periodic solutions, both standing and traveling; 2) long-time well-posedness results; 3) modulational instability of Stokes waves. These results rely on unconventional approaches to KAM and Birkhoff normal form theories for Hamiltonian quasi-linear PDEs and symplectic Kato perturbation theory for separated eigenvalues of reversible and Hamiltonian operators. |
| title | Long time dynamics of space periodic water waves |
| topic | Analysis of PDEs 76B15, 37K55, 35R35, 35C07, 35P05, 37J40 |
| url | https://arxiv.org/abs/2512.22115 |