168 citations · 325 across the 23 of their papers we have counts for
25 papers
An explicit formula for the Benjamin--Ono equation
Patrick Gerard
We establish an explicit formula for the general solution of the Benjamin-Ono equation on the torus and on the line. Contents 1. Introduction 1 1.1. The Benjamin-Ono equation 1 1.2…
On the Benjamin-Ono equation on and its periodic and quasiperiodic solutions
Patrick Gérard, Thomas Kappeler, Petar Topalov
In this paper, we survey our recent results on the Benjamin-Ono equation on the torus. As an application of the methods developed we construct large families of periodic or quasipe…
On a damped Szego equation (with an appendix in collaboration with Christian Klein)
Patrick Gerard, Sandrine Grellier
We investigate how damping the lowest Fourier mode modifies the dynamics of the cubic Szeg{ö} equation. We show that there is a nonempty open subset of initial data generating traj…
On the flow map of the Benjamin-Ono equation on the torus
Patrick Gerard, Thomas Kappeler, Peter Topalov
We prove that for any , the Benjamin--Ono equation on the torus is globally in time well-posed on the Sobolev space $H^{-s}(\T, \R)$,in the sense that the soluti…
The structure of Schmidt subspaces of Hankel operators: a short proof
Alexander Pushnitski, Patrick Gerard
We give a short proof of the main result of our previous paper [2]: every Schmidt subspace of a Hankel operator is the image of a model space by an isometric multiplier. This class…
On the integrability of the Benjamin-Ono equation on the torus
Patrick Gerard, Thomas Kappeler
In this paper we prove that the Benjamin-Ono equation, when considered on the torus, is an integrable (pseudo)differential equation in the strongest possible sense: it admits globa…