4 citations · 8 across the 6 of their papers we have counts for
7 papers
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…
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 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 the spectrum of the Lax operator of the Benjamin-Ono equation on the torus
Patrick Gérard, Thomas Kappeler, Peter Topalov
We investigate the spectrum of the Lax operator of the Benjamin-Ono equation on the torus for complex valued potentials in the Sobolev space $H^{-s}(\mathbb{T},\mathbb{C}…
On the non-existence of local Birkhoff coordinates for the focusing NLS equation
T. Kappeler, P. Topalov
We prove that there exist potentials so that near them the focusing non-linear Schrödinger equation does not admit local Birkhoff coordinates. The proof is based on the constructio…
Spatial asymptotic expansions in the incompressible Euler equation
R. McOwen, Peter Topalov
In this paper we prove that the Euler equation describing the motion of an ideal fluid in is well-posed in a class of functions allowing spatial asymptotic expansions as $|x…
From K.A.M. Tori to Isospectral Invariants and Spectral Rigidity of Billiard Tables
G. Popov, P. Topalov
This article is a part of a project investigating the relationship between the dynamics of completely integrable or close to completely integrable billiard tables, the integral geo…