计算与应用讨论班-Computational methods for the dynamics of the nonlinear Schroedinger/Gross-Pitaevskii equations
2023-10-19 10:00:41
2023-10-19 10:00:41
2023-10-19 10:00:41
Speaker : Weizhu Bao, National University of Singapore
Time : 2023-10-19 10:00:41
Location : 204 Haina Complex Building 2
Abstract:
In this talk, I begin wtih the (nonlinear) Schroedinger/Gross-Pitaevskii equations (NLSE/GPE) for modeling Bose-Einstein condensation (BEC), nonlinear optics, quantum physics and chemistry, 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 difference time domain (FDTD) methods and time-splitting spectral (TSSP) method, and their error estimates and comparison will be discussed. Extensions to NLSE/GPE with an angular momentum rotation term, non-local dipole-dipole interaction, multi-component and logarithmic nonlinearity will be presented.
Applications to soliton interactions, collapse and explosion of BEC, quantum transport and quantized vortex interaction will be investigated.
Finally, I will report our very recent results of energy regularization methods for NLSE with logarithmic nonlinearity and improved uniform error bounds on TSSP for the long-time dynamics of NLSE by using the regularization compensation oscillatory (RCO) technique.