15 citations · 69 across the 12 of their papers we have counts for
4 papers · 2 filters
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…
On the analyticity of the nonlinear Fourier transform of the Benjamin-Ono equation on
P. Gérard, T. Kappeler, P. Topalov
We prove that the nonlinear Fourier transform of the Benjamin-Ono equation on , also referred to as Birkhoff map, is a real analytic diffeomorphism from the scale of So…
On smoothing properties and Tao's gauge transform of the Benjamin-Ono equation on the torus
Patrick Gérard, Thomas Kappeler, Peter Topalov
We prove smoothing properties of the solutions of the Benjamin-Ono equation in the Sobolev space for any . To this end we show that Tao's gau…
On the analytic Birkhoff normal form of the Benjamin-Ono equation and applications
P. Gérard, T. Kappeler, P. Topalov
In this paper we prove that the Benjamin-Ono equation admits an analytic Birkhoff normal form in an open neighborhood of zero in $H^{s}_{0}(\T, \R)$ for any where $H^{s}_{…