| eBook ISBN: | 978-0-8218-8152-1 |
| Product Code: | CONM/473.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| eBook ISBN: | 978-0-8218-8152-1 |
| Product Code: | CONM/473.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
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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 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.
ReadershipGraduate students and research mathematicians interested in various aspects of nonlinear equations and their use in mathematical physics.
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Table of Contents
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Articles
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Weizhu Bao — Analysis and efficient computation for the dynamics of two-component Bose-Einstein condensates [ MR 2522012 ]
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Natalia G. Berloff — Quantised vortices, travelling coherent structures and superfluid turbulence [ MR 2522013 ]
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Fabrice Béthuel, Philippe Gravejat and Jean-Claude Saut — Existence and properties of travelling waves for the Gross-Pitaevskii equation [ MR 2522014 ]
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Rémi Carles — On the semi-classical limit for the nonlinear Schrödinger equation [ MR 2522015 ]
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Patrick Gérard — The Gross-Pitaevskii equation in the energy space [ MR 2522016 ]
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Kenji Nakanishi — Scattering theory for the Gross-Pitaevskii equation [ MR 2522017 ]
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Dmitry E. Pelinovsky and Panayotis G. Kevrekidis — Periodic oscillations of dark solitons in parabolic potentials [ MR 2522018 ]
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Additional Material
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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 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.
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 two-component Bose-Einstein condensates [ MR 2522012 ]
-
Natalia G. Berloff — Quantised vortices, travelling coherent structures and superfluid turbulence [ MR 2522013 ]
-
Fabrice Béthuel, Philippe Gravejat and Jean-Claude Saut — Existence and properties of travelling waves for the Gross-Pitaevskii equation [ MR 2522014 ]
-
Rémi Carles — On the semi-classical limit for the nonlinear Schrödinger equation [ MR 2522015 ]
-
Patrick Gérard — The Gross-Pitaevskii equation in the energy space [ MR 2522016 ]
-
Kenji Nakanishi — Scattering theory for the Gross-Pitaevskii equation [ MR 2522017 ]
-
Dmitry E. Pelinovsky and Panayotis G. Kevrekidis — Periodic oscillations of dark solitons in parabolic potentials [ MR 2522018 ]
