Long time stability for cubic nonlinear Schr\"odinger equations on non-rectangular flat tori
Analysis of PDEs
2025-06-25 v2 Dynamical Systems
Abstract
We consider nonlinear Schr\"odinger equations on flat tori satisfying a simple and explicit Diophantine non-degeneracy condition. Provided that the nonlinearity contains a cubic term, we prove the almost global existence and stability of most of the small solutions in high regularity Sobolev spaces. To this end, we develop a normal form approach designed to handle general resonant Hamiltonian partial differential equations for which it is possible to modulate the frequencies by using the initial data.
Keywords
Cite
@article{arxiv.2402.04122,
title = {Long time stability for cubic nonlinear Schr\"odinger equations on non-rectangular flat tori},
author = {Joackim Bernier and Nicolas Camps},
journal= {arXiv preprint arXiv:2402.04122},
year = {2025}
}