Zobrazeno 1 - 10
of 232
pro vyhledávání: '"Kappeler, Thomas"'
Autor:
Kappeler, Thomas, Montalto, Riccardo
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 to a remainder term, which is smoothing to any given order, the coord
Externí odkaz:
http://arxiv.org/abs/2109.02489
We prove smoothing properties of the solutions of the Benjamin-Ono equation in the Sobolev space $H^{s}(\mathbb{T},\mathbb{R})$ for any $s\ge 0$. To this end we show that Tao's gauge transform is a high frequency approximation of the nonlinear Fourie
Externí odkaz:
http://arxiv.org/abs/2109.00610
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 quasiperiodic solutions, which are not $C^\infty$-smooth.
Externí odkaz:
http://arxiv.org/abs/2103.09291
Autor:
Kappeler, Thomas, Montalto, Riccardo
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 size $\varepsilon > 0$, a large class of periodic multi-solitons of the
Externí odkaz:
http://arxiv.org/abs/2009.02721
Two-sided bounds for the efficiency of the torsion function are obtained in terms of the square of the distance to the boundary function under the hypothesis that the Dirichlet Laplacian satisfies a strong Hardy inequality. Localisation properties of
Externí odkaz:
http://arxiv.org/abs/2008.07167
We investigate the spectrum of the Lax operator $L_u$ of the Benjamin-Ono equation on the torus for complex valued potentials $u$ in the Sobolev space $H^{-s}(\mathbb{T},\mathbb{C})$, $0 \le s < 1/2$, with small imaginary part and prove analytic prop
Externí odkaz:
http://arxiv.org/abs/2006.11864
Autor:
Kappeler, Thomas, Widmer, Yannick
The spectral curve associated with the sinh-Gordon equation on the torus is defined interms of the spectrum of the Lax operator appearing in the Lax pair formulation of the equation. If thespectrum is simple, it is an open Riemann surface of infinite
Externí odkaz:
http://arxiv.org/abs/2003.09194
Autor:
Kappeler, Thomas, Topalov, Peter
We prove an infinite dimensional version of the Arnold-Liouville theorem for integrable non-linear PDEs: In a case study we consider the {\em focusing} NLS equation with periodic boundary conditions.
Externí odkaz:
http://arxiv.org/abs/2002.11638
We prove that for any $0 < s < 1/2$, the Benjamin--Ono equation on the torus is globally in time $C^0-$well-posed on the Sobolev space $H^{-s}(\T, \R)$,in the sense that the solution map, which is known to be defined for smooth data, continuously ext
Externí odkaz:
http://arxiv.org/abs/1909.07314
In this paper we prove the persistence of space periodic multi-solitons of arbitrary size under any quasi-linear Hamiltonian perturbation, which is smooth and sufficiently small. This answers positively a longstanding question whether KAM techniques
Externí odkaz:
http://arxiv.org/abs/1908.08768