L. Chaichenets

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math.AP2019

On the global well-posedness of the quadratic NLS on $L^{2} (R) + H^{1} (T)$

Leonid Chaichenets, Dirk Hundertmark, Peer Christian Kunstmann +1

We study the one dimensional nonlinear Schrödinger equation with power nonlinearity $∣ u ∣^{α - 1} u$ for $α \in [1, 5]$ and initial data $u_{0} \in L^{2} (R) + H^{1} (T)$ . We…

math.AP2019

The global Cauchy problem for the NLS with higher order anisotropic dispersion

Leonid Chaichenets, Nikolaos Pattakos

We use a method developed by Strauss to obtain global wellposedness results in the mild sense for the small data Cauchy problem in modulation spaces $M_{p, q}^{s} (R^{d})$ , wher…

math.AP2018

Knocking out teeth in one-dimensional periodic NLS

Leonid Chaichenets, Dirk Hundertmark, Peer Kunstmann +1

We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic nonlinear Schrödinger equation in one dimension with initial data $u_{0}$ in $H^{s…