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

2023/12/05 by Bambusi, Dario, Gérard, Patrick · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.02833

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 ε 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(ε^(1)/(2(N+1))) close to their initial value for times exponentially long with ε^{-(1)/(2(N+1))}.

Cited by

• Almost global existence for Ultra-differential Hamiltonian in L² space
• Nekhoroshev type stability for non-local semilinear Schrödinger equations

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