We study the dynamics of a spin-1/2 XXZ chain which is initially prepared in a domain-wall
state. We compare the results of time-dependent Density Matrix Renormalization Group …

In this paper, we study the evolution of the vortex filament equation (VFE), $$\mathbf
X_t=\mathbf X_s\wedge\mathbf X_ {ss}, $$ with $\mathbf X (s, 0) $ being a regular planar …

We introduce a numerical approach to computing the Schrödinger map (SM) based on the
Hasimoto transform which relates the SM flow to a cubic nonlinear Schrödinger (NLS) …

Scattering for 1D cubic NLS and singular vortex dynamics Page 1 DOI 10.4171/JEMS/300 J.
Eur. Math. Soc. 14, 209–253 c European Mathematical Society 2012 Valeria Banica · Luis …

In this paper we continue our investigation of self-similar solutions of the vortex filament
equation, also known as the binormal flow or the localized induction equation. Our main …

In this article we consider the initial value problem of the binormal flow with initial data given
by curves that are regular except at one point where they have a corner. We prove that …

In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a
regular M-corner polygon as initial datum can be explained at infinitesimal times as the …

This paper focuses on surveying some recent results obtained by the author together with V.
Banica on the evolution of a vortex filament with one corner according to the so-called …

In this paper, we consider the evolution of the vortex filament equation (VFE):
X_t=X_s∧X_ss, taking M-sided regular polygons with nonzero torsion as initial data. Using …

The aim of this paper is twofold. First, we show the evolution of the vortex filament equation
(VFE) for a regular planar polygon in the hyperbolic space. Unlike in the Euclidean space …