Long time dynamics of space periodic water waves
Analysis of PDEs
2025-12-29 v1
Abstract
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.
Cite
@article{arxiv.2512.22115,
title = {Long time dynamics of space periodic water waves},
author = {Massimiliano Berti},
journal= {arXiv preprint arXiv:2512.22115},
year = {2025}
}
Comments
Accepted for the ICM2026 Proceedings to be published by SIAM