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A Nekhoroshev theorem for some perturbations of the Benjamin-Ono equation with initial data close to finite gap tori
Dario Bambusi, Patrick Gérard
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 correspon…
On the low regularity phase space of the Benjamin-Ono equation
Patrick Gérard, Peter Topalov
In this paper we prove that the Benjamin-Ono equation is globally in time -well-posed in the Hilbert space of periodic distributi…
The zero dispersion limit for the Benjamin--Ono equation on the line
Patrick Gérard
We identify the zero dispersion limit of a solution of the Benjamin--Ono equation on the line corresponding to every initial datum in . We infer a maximu…
The cubic Szegő equation on the real line: explicit formula and well-posedness on the Hardy class
Patrick Gérard, Alexander Pushnitski
We establish an explicit formula for the solution of the the cubic Szegő equation on the real line. Using this formula, we prove that the evolution flow of this equation can be con…