We consider two-dimensional Bose–Einstein condensates with attractive interaction,
described by the Gross–Pitaevskii functional. Minimizers of this functional exist only if the …

Abstract The Gross–Pitaevskii equation (GPE) is discussed at the level of an advanced
course on statistical physics. In the standard literature the GPE is usually obtained in the …

We propose the critical nonlinear Schrödinger equation with a harmonic potential as a
model of attractive Bose–Einstein condensates. By an elaborate mathematical analysis we …

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-
dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on …

Dark soliton states of Bose-Einstein condensates in harmonic traps are studied both
analytically and computationally by the direct solution of the Gross-Pitaevskii equation in …

We are interested in the attractive Gross-Pitaevskii (GP) equation in $\R^ 2$, where the
external potential $ V (x) $ vanishes on $ m $ disjoint bounded domains …

We calculated, within the Gross-Pitaevskii formalism, the critical number of atoms for Bose-
Einstein condensates with two-body attractive interactions in cylindrical traps with different …

The collapsing dynamics of a trapped Bose-Einstein condensate with attractive interaction
are revealed to exhibit two previously unknown phenomena. During the collapse, the …

We study certain stationary and time-evolution problems of trapped Bose-Einstein
condensates using the numerical solution of the Gross-Pitaevskii (GP) equation with both …

The statistical equilibria of the (conservative) dynamics of the Gross-Pitaevskii equation
(GPE) with a finite range of spatial Fourier modes are characterized using a new algorithm …