We obtain analytic solutions to the Gross-Pitaevskii equation with negative scattering length
in highly asymmetric traps. We find that in these traps the Bose-Einstein condensates …

A variational technique is applied to solve the time-dependent nonlinear Schrödinger equation
(Gross-Pitaevskii equation) with the goal to model the dynamics of dilute ultracold atom …

We solve the time-dependent Gross-Pitaevskii equation by a variational ansatz to calculate
the excitation spectrum of a Bose-Einstein condensate in a trap. The trial wave function is a …

We present a new numerical scheme for nonlinear Schrödinger type equations. The scheme
conserves the energy and charge of the systems and it is linearly implicit. Numerical …

Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schrödinger
equations with potentials and nonlinearities depending both on time and on the spatial …

We study a four-level atomic system with electromagnetically induced transparency with
giant χ (3) and χ (5) susceptibilities of opposite signs. This system will allow us to obtain …

Using Lie group theory and canonical transformations, we construct explicit solutions of
nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities. We present the …

We demonstrate, through numerical simulations, the controllable emission of matter-wave
bursts from a Bose-Einstein condensate in a shallow optical dipole trap. The process is …

In this paper, we propose a numerical method to approximate the solution of partial differential
equations in irregular domains with no-flux boundary conditions. The idea is to embed the …

Background: Glioblastoma (GBM) is one of the most lethal tumor types. Hypercellular regions,
named pseudopalisades, are characteristic in these tumors and have been hypothesized …