【摘 要】
：
In this talk, I begin wtih the nonlinear Schrodinger/Gross-Pitaevskii equations (NLSE/GPE) for modeling Bose-Einstein condensation (BEC), nonlinear optics, etc.
【机 构】
：
DepartmentofMathematicsNationalUniversityofSingapore
【出 处】
：
中国科学院第七届海峡两岸及国际量子调控会议
论文部分内容阅读
In this talk, I begin wtih the nonlinear Schrodinger/Gross-Pitaevskii equations (NLSE/GPE) for modeling Bose-Einstein condensation (BEC), nonlinear optics, etc., and review some dynamical properties of NLSE/GPE including conserved quantities, dispersion relation, center-of-mass dynamics,soliton solutions and semiclassical limits.Different numerical methods will be presented including finite different time domain (FDTD) methods and time-splitting spectral method, and their error estimates and comparison will be discussed.Extensions to NLSE/GPE with an angular momentum rotation term and/or non-local dipole-dipole interaction as well as multi-component will be presented.Finally, applications to soliton interactions, collapse and explosion of BEC, quantum transport and quantized vortex interaction will be investigated.
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