Zobrazeno 1 - 10
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pro vyhledávání: '"Kappeler, T."'
We prove that the nonlinear Fourier transform of the Benjamin-Ono equation on $\mathbb{T}$, also referred to as Birkhoff map, is a real analytic diffeomorphism from the scale of Sobolev spaces $H^{s}_{0}(\mathbb{T},\mathbb{R})$, $s > -1/2$, to the sc
Externí odkaz:
http://arxiv.org/abs/2109.08988
Autor:
Koegel, A., Furet, C., Suzuki, T., Klebanov, Y., Hu, J., Kappeler, T., Okazaki, D., Matsui, K., Hiraoka, T., Shimono, K., Nakano, K., Honma, K., Pennington, M.
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 to this information can inform their decision making, and enable them t
Externí odkaz:
http://arxiv.org/abs/2107.01763
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 $s>-1/2$ where $H^{s}_{0}(\T, \R)$ denotes the subspace of the Sobolev space $H^{s}(\T, \R)$
Externí odkaz:
http://arxiv.org/abs/2103.07981
We consider the torsion function for the Dirichlet Laplacian $-\Delta$, and for the Schr\"odinger operator $- \Delta + V$ on an open set $\Omega\subset \R^m$ of finite Lebesgue measure $0<|\Omega|<\infty$ with a real-valued, non-negative, measurable
Externí odkaz:
http://arxiv.org/abs/2005.06366
We prove that the Benjamin--Ono equation on the torus is globally in time well-posed in the Sobolev space $H^{s}(\mathbb{T},\mathbb{R})$ for any $s > - 1/2$ and ill-posed for $s \le - 1/2$. Hence the critical Sobolev exponent $s_c=-1/2$ of the Benjam
Externí odkaz:
http://arxiv.org/abs/2004.04857
Autor:
Kappeler, T., Topalov, P.
We prove that there exist potentials so that near them the focusing non-linear Schr\"odinger equation does not admit local Birkhoff coordinates. The proof is based on the construction of a local normal form of the linearization of the equation at suc
Externí odkaz:
http://arxiv.org/abs/1807.02455
In this paper we prove approximation properties of the solutions of the defoucsing NLS equation on the circle by nearly linear flows. In addition we show that spatially periodic solutions of the defocusing NLS equation evolving in fractional Sobolev
Externí odkaz:
http://arxiv.org/abs/1505.07394
In this paper we prove that the non-linear Fourier transform of the defocusing NLS equation on the circle is linear up to terms which are one order smoother.
Externí odkaz:
http://arxiv.org/abs/1505.04455
In this paper we provide new asymptotic estimates of various spectral quantities of Zakharov-Shabat operators on the circle. These estimates are uniform on bounded subsets of potentials in Sobolev spaces.
Externí odkaz:
http://arxiv.org/abs/1503.04850
Autor:
Kappeler, T., Topalov, P.
We develop a new approach for constructing normalized differentials on hyperelliptic curves of infinite genus and obtain uniform asymptotic estimates for the distribution of their zeros.
Externí odkaz:
http://arxiv.org/abs/1408.7107