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arXiv · 2312.02833

A Nekhoroshev theorem for some perturbations of the Benjamin-Ono equation with initial data close to finite gap tori

Dario Bambusi·Patrick Gérard
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Abstract

We consider a perturbation of the Benjamin Ono equation with periodic boundary conditions on a segment. We consider the case where the perturbation is Hamiltonian and the corresponding Hamiltonian vector field is analytic as a map form energy space to itself. Let $\epsilon$ be the size of the perturbation. We prove that for initial data close in energy norm to an $N$-gap state of the unperturbed equation all the actions of the Benjamin Ono equation remain $\cO(\epsilon^{\frac{1}{2(N+1)}})$ close to their initial value for times exponentially long with $\epsilon^{-\frac{1}{2(N+1)}}$.

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Dario Bambusi, Patrick Gérard. 2023-12-05. A Nekhoroshev theorem for some perturbations of the Benjamin-Ono equation with initial data close to finite gap tori. https://arxiv.org/abs/2312.02833

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