eBook ISBN:  9780821881521 
Product Code:  CONM/473.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821881521 
Product Code:  CONM/473.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 473; 2008; 180 ppMSC: Primary 35; 37
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 oneweek 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 semiclassical limit, scattering theory, existence and properties of coherent traveling structures, and numerical simulations.
ReadershipGraduate students and research mathematicians interested in various aspects of nonlinear equations and their use in mathematical physics.

Table of Contents

Articles

Weizhu Bao — Analysis and efficient computation for the dynamics of twocomponent BoseEinstein condensates [ MR 2522012 ]

Natalia G. Berloff — Quantised vortices, travelling coherent structures and superfluid turbulence [ MR 2522013 ]

Fabrice Béthuel, Philippe Gravejat and JeanClaude Saut — Existence and properties of travelling waves for the GrossPitaevskii equation [ MR 2522014 ]

Rémi Carles — On the semiclassical limit for the nonlinear Schrödinger equation [ MR 2522015 ]

Patrick Gérard — The GrossPitaevskii equation in the energy space [ MR 2522016 ]

Kenji Nakanishi — Scattering theory for the GrossPitaevskii equation [ MR 2522017 ]

Dmitry E. Pelinovsky and Panayotis G. Kevrekidis — Periodic oscillations of dark solitons in parabolic potentials [ MR 2522018 ]


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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 oneweek 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 semiclassical limit, scattering theory, existence and properties of coherent traveling structures, and numerical simulations.
Graduate students and research mathematicians interested in various aspects of nonlinear equations and their use in mathematical physics.

Articles

Weizhu Bao — Analysis and efficient computation for the dynamics of twocomponent BoseEinstein condensates [ MR 2522012 ]

Natalia G. Berloff — Quantised vortices, travelling coherent structures and superfluid turbulence [ MR 2522013 ]

Fabrice Béthuel, Philippe Gravejat and JeanClaude Saut — Existence and properties of travelling waves for the GrossPitaevskii equation [ MR 2522014 ]

Rémi Carles — On the semiclassical limit for the nonlinear Schrödinger equation [ MR 2522015 ]

Patrick Gérard — The GrossPitaevskii equation in the energy space [ MR 2522016 ]

Kenji Nakanishi — Scattering theory for the GrossPitaevskii equation [ MR 2522017 ]

Dmitry E. Pelinovsky and Panayotis G. Kevrekidis — Periodic oscillations of dark solitons in parabolic potentials [ MR 2522018 ]