We study the process of dispersion of low-regularity solutions to the Schrödinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get ...

We describe invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schr\"odinger equation (DNLS) constructed in \cite{MR3518561, Genovese2018}. The construction works for small $L^2$ ...

The main task of this thesis is the analysis of the initial data u0 of Schrödinger’s initial value problem in order to determine certain properties of its dynamical evolution. First we consider the elliptic Schrödinger ...

Riemann's non-differentiable function is a classic example of a continuous but almost nowhere differentiable function, whose analytic regularity has been widely studied since it was proposed in the second half of the 19th ...

In this thesis, first, we propose a novel pseudospectral method to approximate accu- rately and efficiently the fractional Laplacian without using truncation. More pre- cisely, given a bounded regular function defined over ...

In this article we deduce necessary and sufficient conditions for the presence of “Conti-type”, highly symmetric, exactly stress-free constructions in the geometrically non-linear, planar n-well problem, generalising results ...

One of the most interesting phenomena in fluid literature is the occurrence and evolution of vortex filaments. Some of their examples in the real world are smoke rings, whirlpools, and tornadoes. For an ideal fluid, there ...

Riemann’s non-differentiable function is a classic example of a continuous function which is almost nowhere differentiable, and many results concerning its analytic regularity have been shown so far. However, it can also ...

The stress required for the propagation of twin boundaries in a sample with fine twins increases monotonically with ongoing deformation. In contrast, for samples with a single twin boundary, the stress exhibits a plateau ...

The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schr ̈odinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. ...