# Stationary and Time Dependent Gross-Pitaevskii Equations

Share this page *Edited by *
*Alberto Farina; Jean-Claude Saut*

This volume is based on a thematic program on the
Gross–Pitaevskii equation, which was held at the Wolfgang Pauli
Institute in Vienna in 2006. The program consisted of two workshops
and a one-week Summer School.

The Gross–Pitaevskii equation, an example of a defocusing
nonlinear Schrödinger equation, is a model for phenomena such as
the Bose–Einstein condensation of ultra cold atomic gases, the
superfluidity of Helium II, or the “dark solitons” of
Nonlinear Optics. Many interesting and difficult mathematical
questions associated with the Gross–Pitaevskii equation, linked
for instance to the nontrivial boundary conditions at infinity, arise
naturally from its modeling aspects.

The articles in this volume review some of the recent developments in the
theory of the Gross–Pitaevskii equation. In particular the following
aspects are considered: modeling of superfluidity and Bose–Einstein
condensation, the Cauchy problem, the semi-classical limit, scattering
theory, existence and properties of coherent traveling structures, and
numerical simulations.

#### Readership

Graduate students and research mathematicians interested in various aspects of nonlinear equations and their use in mathematical physics.

# Table of Contents

## Stationary and Time Dependent Gross-Pitaevskii Equations

- Contents v6 free
- Preface vii8 free
- Analysis and efficient computation for the dynamics of two-component Bose-Einstein condensates 110 free
- Quantised vortices, travelling coherent structures and superfluid turbulence 2736
- Existence and properties of travelling waves for the Gross-Pitaevskii equation 5564
- Periodic oscillations of dark solitons in parabolic potentials 159168