15 citations · 69 across the 12 of their papers we have counts for
14 papers
Soliton and breather resolution for the cubic Szegö flow on the line
Patrick Gerard, Sandrine Grellier
We investigate the long time behaviour of the solutions of the cubic Szeg}o equation on the line in the Sobolev space H^{1/2}(R). We prove that, for every datum of which the Lax op…
The Calogero--Moser Derivative Nonlinear Schrödinger Equation
Patrick Gérard, Enno Lenzmann
We study the Calogero--Moser derivative NLS equation posed on the Hardy-Sobolev space with suitable…
Unbounded Hankel operators and the flow of the cubic Szegő equation
Patrick Gérard, Alexander Pushnitski
We prove that, for any Hankel operator with a symbol from the Hardy class , the maximal and minimal domains coincide. As an application, we prove that the evolution flow of th…
The Lax pair structure for the spin Benjamin--Ono equation
Patrick Gérard
We prove that the recently introduced spin Benjamin--Ono equation admits a Lax pair, and we deduce a family of conservation laws which allow to prove global wellposedness in all So…
An inverse problem for Hankel operators and turbulent solutions of the cubic Szegő equation on the line
Patrick Gérard, Alexander Pushnitski
We construct inverse spectral theory for finite rank Hankel operators acting on the Hardy space of the upper half-plane. A particular feature of our theory is that we completely ch…
Turbulent cascades for a family of damped Szegö equations
Patrick Gérard, Sandrine Grellier, Zihui He
In this paper, we study the transfer of energy from low to high frequencies for a family of damped Szegö equations. The cubic Szegö equation has been introduced as a toy model for…