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pro vyhledávání: '"Klaus, Friedrich"'
We prove a version of wellposedness for all equations of the KdV hierarchy in $H^{-1}$. Ingredients are 1) The Miura map which allows to define the Gardner hierarchy through the generating function of the energies so that the $N$th Gardner equation i
Externí odkaz:
http://arxiv.org/abs/2309.12773
Autor:
Klaus, Friedrich
In this work we prove a Strichartz estimate for the Schr\"odinger equation in the quasiperiodic setting. We also show a lower bound on the number of resonant frequency interactions in this situation.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/2306.07086
Autor:
Klaus, Friedrich
In this work we consider integrable PDE with higher dimensional Lax pairs. Our main example is a quadratic dNLS equation with a $3 \times 3$ Lax pair. For this equation we show a-priori estimates in Sobolev spaces of negative regularity $H^s(\mathbb{
Externí odkaz:
http://arxiv.org/abs/2305.11524
Autor:
Klaus, Friedrich
We prove new local and global well-posedness results for the cubic one-dimensional nonlinear Schr\"odinger equation in modulation spaces. Local results are obtained via multilinear interpolation. Global results are proven using conserved quantities b
Externí odkaz:
http://arxiv.org/abs/2204.04957
Autor:
Klaus, Friedrich, Kunstmann, Peer
We show global wellposedness for the defocusing cubic nonlinear Schr\"odinger equation (NLS) in $H^1(\mathbb{R}) + H^{3/2+}(\mathbb{T})$, and for the defocusing NLS with polynomial nonlinearities in $H^1(\mathbb{R}) + H^{5/2+}(\mathbb{T})$. This comp
Externí odkaz:
http://arxiv.org/abs/2109.11341