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Pré-Publication, Document De Travail Année : 2024

Long time stability for cubic nonlinear Schr\"odinger equations on non-rectangular flat tori

Joackim Bernier
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Nicolas Camps

Résumé

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.

Dates et versions

hal-04443016 , version 1 (07-02-2024)

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Joackim Bernier, Nicolas Camps. Long time stability for cubic nonlinear Schr\"odinger equations on non-rectangular flat tori. 2024. ⟨hal-04443016⟩
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