The semiclassically scaled time-dependent multi-particle Schrödinger equation describes,
inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational …

Along with finite differences and finite elements, spectral methods are one of the three main
methodologies for solving partial differential equations on computers. This book provides a …

Madelung, Gross--Pitaevskii and Korteweg Page 1 Nonlinearity PAPER Madelung, Gross–Pitaevskii
and Korteweg To cite this article: Rémi Carles et al 2012 Nonlinearity 25 2843 View the …

In this paper, we mainly review recent results on mathematical theory and numerical
methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation …

In this paper, we begin with the nonlinear Schrödinger/Gross–Pitaevskii equation
(NLSE/GPE) for modeling Bose–Einstein condensation (BEC) and nonlinear optics as well …

We study the numerical solution of the time-dependent Gross–Pitaevskii equation (GPE)
describing a Bose–Einstein condensate (BEC) at zero or very low temperature. In …

This book expands lecture notes by the authors for a course on Introduction of Spectral
Methods taught in the past few years at Penn State University, Simon Fraser University, the …

In this paper, we present a continuous normalized gradient flow (CNGF) and prove its
energy diminishing property, which provides a mathematical justification of the imaginary …

Here we develop simple numerical algorithms for both stationary and non-stationary
solutions of the time-dependent Gross–Pitaevskii (GP) equation describing the properties of …

We present the asymptotic transitions from microscopic to macroscopic physics, their
computational challenges and the asymptotic-preserving (AP) strategies to compute …