Long time stability for cubic nonlinear Schrödinger equations on non-rectangular flat tori
Abstract
We consider nonlinear Schrödinger 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2024
- DOI:
- 10.48550/arXiv.2402.04122
- arXiv:
- arXiv:2402.04122
- Bibcode:
- 2024arXiv240204122B
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematics - Dynamical Systems;
- 35B34;
- 35B35;
- 35Q55;
- 37K45;
- 37K55