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arXiv · 2309.14276

Almost-periodic solutions to the NLS equation with smooth convolution potentials

Livia Corsi·Guido Gentile·Michela Procesi
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Abstract

We consider the one-dimensional NLS equation with a convolution potential and a quintic nonlinearity. We prove that, for most choices of potentials with polynomially decreasing Fourier coefficients, there exist almost-periodic solutions in the Gevrey class with frequency satisfying a Bryuno non-resonance condition. This allows convolution potentials of class $C^p$, for any integer $p$: as far as we know this is the first result where the regularity of the potential is arbitrarily large and not compensated by a corresponding smoothing of the nonlinearity.

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Livia Corsi, Guido Gentile, Michela Procesi. 2023-09-25. Almost-periodic solutions to the NLS equation with smooth convolution potentials. https://arxiv.org/abs/2309.14276

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