《博士后文庫》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 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 編后記 Appendix
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