[PDF][PDF] A general review on the NLS equation with point-concentrated nonlinearity

L Tentarelli - Commun. Appl. Ind. Math, 2023 - intapi.sciendo.com
The paper presents a complete (to the best of the author's knowledge) overview on the
existing literature concerning the NLS equation with point-concentrated nonlinearity …

Quantum droplets in two-dimensional optical lattices

YY Zheng, ST Chen, ZP Huang, SX Dai, B Liu, YY Li… - Frontiers of …, 2021 - Springer
We study the stability of zero-vorticity and vortex lattice quantum droplets (LQDs), which are
described by a two-dimensional (2D) Gross–Pitaevskii (GP) equation with a periodic …

Ground states for the planar NLSE with a point defect as minimizers of the constrained energy

R Adami, F Boni, R Carlone, L Tentarelli - Calculus of Variations and …, 2022 - Springer
We investigate the ground states for the focusing, subcritical nonlinear Schrödinger equation
with a point defect in dimension two, defined as the minimizers of the energy functional at …

Suppression of the quasi-two-dimensional quantum collapse in the attraction field by the Lee-Huang-Yang effect

E Shamriz, Z Chen, BA Malomed - Physical Review A, 2020 - APS
Quantum collapse in three and two dimensions (3D and 2D) is induced by attractive
potential∼− r− 2. It was demonstrated that the mean-field (MF) cubic self-repulsion in the 3D …

Exact solutions to fall of particle to singular potential: Classical versus quantum cases

MI Tribelsky - Proceedings of the Royal Society A, 2023 - royalsocietypublishing.org
Exact solutions describing a fall of a particle to the centre of a non-regularized singular
potential in classical and quantum cases are obtained and compared. We inspect the …

Two-dimensional vortex quantum droplets get thick

Z Lin, X Xu, Z Chen, Z Yan, Z Mai, B Liu - Communications in Nonlinear …, 2021 - Elsevier
We study two-dimensional (2D) vortex quantum droplets (QDs) trapped by a thicker
transverse confinement with a⊥> 1 μ m. Under this circumstance, the Lee-Huang-Yang …

Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect

R Adami, F Boni, R Carlone, L Tentarelli - Journal of Mathematical …, 2022 - pubs.aip.org
We study the ground states for the Schrödinger equation with a focusing nonlinearity and a
point interaction in dimension three. We establish that ground states exist for every value of …

Well posedness of the nonlinear Schrödinger equation with isolated singularities

C Cacciapuoti, D Finco, D Noja - Journal of Differential Equations, 2021 - Elsevier
We study the well posedness of the nonlinear Schrödinger (NLS) equation with a point
interaction and power nonlinearity in dimension two and three. Behind the autonomous …

Double-layer Bose-Einstein condensates: A quantum phase transition in the transverse direction, and reduction to two dimensions

MCP Dos Santos, BA Malomed, WB Cardoso - Physical Review E, 2020 - APS
We revisit the problem of the reduction of the three-dimensional (3D) dynamics of Bose-
Einstein condensates, under the action of strong confinement in one direction (z), to a 2D …

An effective equation for quasi-one-dimensional funnel-shaped Bose–Einstein condensates with embedded vorticity

MCP Santos, WB Cardoso, BA Malomed - The European Physical Journal …, 2022 - Springer
On the basis of a recently introduced model for the Bose–Einstein condensate (BEC)
trapped in the 2D “funnel” potential, ∼∼-r^-1-r-1, we develop analysis for vortex modes …