23 citations · 242 across the 47 of their papers we have counts for
51 papers
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…
Normal form coordinates for the Benjamin-Ono equation having expansions in terms of pseudo-differential operators
Thomas Kappeler, Riccardo Montalto
Near an arbitrary finite gap potential we construct real analytic, canonical coordinates for the Benjamin-Ono equation on the torus having the following two main properties: (1) up…
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…
Exploration of increasing drivers trust in a semi-autonomous vehicle through real time visualizations of collaborative driving dynamic
A. Koegel, C. Furet, T. Suzuki +10
The Thinking Wave is an ongoing development of visualization concepts showing the real-time effort and confidence of semi-autonomous vehicle (AV) systems. Offering drivers access t…
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 stability of periodic multi-solitons of the KdV equation
Thomas Kappeler, Riccardo Montalto
In this paper we obtain the following stability result for periodic multi-solitons of the KdV equation: We prove that under any given semilinear Hamiltonian perturbation of small s…