包邮外势场中玻色-爱因斯坦凝聚体的动力学研究

《博士后文库》序PrefaceIntroductionChapter 1 Theoretical models and methods1．1 Introduction to Bose-Einstein condensates1．2 The Gross-Pitaevskii mean-field models1．2．1 The continuous Gross-Pitaevskii equations1．2．2 The discrete Gross-Pitaevskii equations1．3 Variational approximation approach1．4 Discrete modulational instability analysis1．5 Prolongation structure techniqueBibliographyChapter 2 Variational approximation and modulational instability．2．1 Variational approximation for continuous GP equations2．1．1 Variational approximation for the focusing NLS equation2．1．2 Collective excitations of a 3D BEC in a double-well trap2．2 Variational approximation for discrete Gross-Pitaevskii equations2．3 Discrete modulational instability of discrete Gross- Pitaevskii equationsBibliographyChapter 3 Dynamics of BEC with time- and space-modulated nonlinearities3．1 Linear time-dependent SchrSdinger equation with harmonic potential3．2 One-dimensional BECs with time- and space-modulated nonlinearities3．2．1 One-dimensional BEC with space-modulated nonlinearity3．2．2 Two-component BECs with spatiotemporally modulated nonlinearities3．3 Two-dimensional BEC with time- and space-modulated nonlinearities3．3．1 Quantized quasi-2D BEC with spatially modulated nonlinearity3．3．2 Quantized vortices in a rotating Bose-Einstein condensate3．4 Three-dimensional BEC with space-modulated nonlinearity3．4．1 3D BEC in cylindrically symmetric potential3．4．2 3D BEC in spherically symmetric potentialBibliographyChapter 4 Dynamics of Bose-Einstein condensate with cubicquintic nonlinearity4．1 The theoretical model and its solutions4．2 Stability of nonlinear matter waves in BEC with two-body interaction4．3 Stability of nonlinear matter waves in BEC with two- and three-body interactions4．4 The exact vortex soliton solutions of quasi-two dimensional GP equation4．5 Structures of the vortex solitonsBibliographyChapter 5 Integrability and dynamics of a spin-1 Bose-Einstein condensate5．1 The theoretical model5．2 Integrability and matter-wave solitons in a spin-1 Bose-Einstein condensate5．2．1 Similarity transformation5．2．2 Prolongation structures of the three coupled NLS equation5．3 Matter-wave solitons in F = 1 spinor Bose-Einstein condensate5．3．1 Exact N-bright soliton solutions to the integrable case b2=b05．3．2 Exact N-bright soliton solutions to the integrable case b2=0BibliographyChapter 6 Matter-wave solitons in a spin-1 BEC with time-modulated external potential6．1 The model6．2 Exact matter-wave soliton solutions6．3 Matter-wave solitons in a spin-1 BEC with time-dependent parameters6．3．1 Attractive harmonic potential with constant frequency6．3．2 Expulsive harmonic potential with time-dependent frequency6．3．3 Different choices of the condensate parametersBibliographyChapter 7 Dynamics and stability of the spin-1 BEC in a standing light wave7．1 Spin-1 BEC in a standing light wave7．2 Stationary solutions and linear stability analysis7．2．1 Exact stationary solutions of three-component GP equations．7．2．2 Linear stability analysis7．3 Dynamics and stability7．3．1 Dynamics and stability of the stationary solutions 1～37．3．2 Stability of the stationary solutions 4～57．3．3 Stability of the stationary solutions 6～9BibliographyChapter 8 Summary and future prospects8．1 Summary8．2 Future prospects编后记Appendix