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arXiv · 2208.02040

Reducibility and nonlinear stability for a quasi-periodically forced NLS

Emanuele Haus·Beatrice Langella·Alberto Maspero·Michela Procesi
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Abstract

Motivated by the problem of long time stability vs. instability of KAM tori of the Nonlinear cubic Schr\"odinger equation (NLS) on the two dimensional torus $\mathbb T^2:= (\mathbb R/2\pi \mathbb Z)^2$, we consider a quasi-periodically forced NLS equation on $\mathbb T^2$ arising from the linearization of the NLS at a KAM torus. We prove a reducibility result as well as long time stability of the origin. The main novelty is to obtain the precise asymptotic expansion of the frequencies which allows us to impose Melnikov conditions at arbitrary order.

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Emanuele Haus, Beatrice Langella, Alberto Maspero, Michela Procesi. 2022-08-03. Reducibility and nonlinear stability for a quasi-periodically forced NLS. https://arxiv.org/abs/2208.02040

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