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Computational methods for the dynamics of the nonlinear Schroedinger/Gross-Pitaevskii equations

PDE and Applied Math Seminar

Speaker: Professor Weizhu Bao, National University of Singapore
Related Webpage: https://scholar.google.com/citations?user=24_RZlgAAAAJ&hl=cs
Location: 2112 MSB
Start time: Fri, Oct 5 2018, 4:10PM

In this talk, I begin with 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 semi-classical 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.