外势场中玻色：爱因斯坦凝聚体的动力学研究（英文版）

《博士后文库》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 cubicquintic 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
编后记
Appendix