Long time stability for cubic nonlinear Schrödinger equations on non-rectangular flat tori
arXiv:2402.04122 · doi:10.5802/jep.300
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.
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