稀薄原子氣體中玻色-愛因斯坦凝聚的實現為研
究原子物質波的非線性動力學性質提供了可能性，一
些在非線性光學中熟知的奇異現像不斷在玻色-愛因
斯坦凝聚中被觀察到。在過去二十年間，操控原子間
相互作用的技術引起了人們廣泛的關注。例如，通過
磁場或光場Feshbach共振技術，人們可以有效地調節
原子間的相互作用從而達到操控該繫統的目的，特別
地，在共振磁場附近，繫統會呈現出豐富的新奇量子
物理性質。在平均場理論框架下，稀薄氣體的玻色-
愛因斯坦凝聚體的動力學可以由Gross-Pitaevskii
(GP)方程來描述，該方程的非線性項繫數可以通過磁
場或光場Feshbach共振技術來調制。在《外勢場中玻
色-愛因斯坦凝聚體的動力學研究》中，編者王燈山
基於平均場近似的GP方程來研究外勢場中的具有各種
原子相互作用的玻色-愛因斯坦凝聚體的新奇動力學
。

《博士後文庫》序
Preface
Introduction
Chapter 1 Theoretical models and methods
1.1 Introduction to Bose-Einstein condensates
1.2 The Gross-Pitaevskii mean-field models
1.2.1 The continuous Gross-Pitaevskii equations
1.2.2 The discrete Gross-Pitaevskii equations
1.3 Variational approximation approach
1.4 Discrete modulational instability analysis
1.5 Prolongation structure technique
Bibliography
Chapter 2 Variational approximation and modulational instability.
2.1 Variational approximation for continuous GP equations
2.1.1 Variational approximation for the focusing NLS equation
2.1.2 Collective excitations of a 3D BEC in a double-well trap
2.2 Variational approximation for discrete Gross-Pitaevskii equations
2.3 Discrete modulational instability of discrete Gross- Pitaevskii equations
Bibliography
Chapter 3 Dynamics of BEC with time- and space-modulated nonlinearities
3.1 Linear time-dependent SchrSdinger equation with harmonic potential
3.2 One-dimensional BECs with time- and space-modulated nonlinearities
3.2.1 One-dimensional BEC with space-modulated nonlinearity
3.2.2 Two-component BECs with spatiotemporally modulated nonlinearities
3.3 Two-dimensional BEC with time- and space-modulated nonlinearities
3.3.1 Quantized quasi-2D BEC with spatially modulated nonlinearity
3.3.2 Quantized vortices in a rotating Bose-Einstein condensate
3.4 Three-dimensional BEC with space-modulated nonlinearity
3.4.1 3D BEC in cylindrically symmetric potential
3.4.2 3D BEC in spherically symmetric potential
Bibliography
Chapter 4 Dynamics of Bose-Einstein condensate with cubic-quintic nonlinearity
4.1 The theoretical model and its solutions
4.2 Stability of nonlinear matter waves in BEC with two-body interaction
4.3 Stability of nonlinear matter waves in BEC with two- and three-body interactions
4.4 The exact vortex soliton solutions of quasi-two dimensional GP equation
4.5 Structures of the vortex solitons
Bibliography
Chapter 5 Integrability and dynamics of a spin-1 Bose-Einstein condensate
5.1 The theoretical model
5.2 Integrability and matter-wave solitons in a spin-1 Bose-Einstein condensate
5.2.1 Similarity transformation
5.2.2 Prolongation structures of the three coupled NLS equation
5.3 Matter-wave solitons in F = 1 spinor Bose-Einstein condensate
5.3.1 Exact N-bright soliton solutions to the integrable case b2=b0
5.3.2 Exact N-bright soliton solutions to the integrable case b2=0
Bibliography
Chapter 6 Matter-wave solitons in a spin-1 BEC with time-modulated external potential
6.1 The model
6.2 Exact matter-wave soliton solutions
6.3 Matter-wave solitons in a spin-1 BEC with time-dependent parameters
6.3.1 Attractive harmonic potential with constant frequency
6.3.2 Expulsive harmonic potential with time-dependent frequency
6.3.3 Different choices of the condensate parameters
Bibliography
Chapter 7 Dynamics and stability of the spin-1 BEC in a standing light wave
7.1 Spin-1 BEC in a standing light wave
7.2 Stationary solutions and linear stability analysis
7.2.1 Exact stationary solutions of three-component GP equations.
7.2.2 Linear stability analysis
7.3 Dynamics and stability
7.3.1 Dynamics and stability of the stationary solutions 1～3
7.3.2 Stability of the stationary solutions 4～5
7.3.3 Stability of the stationary solutions 6～9
Bibliography
Chapter 8 Summary and future prospects
8.1 Summary
8.2 Future prospects
編後記
Appendix