Weizhu Bao, Professor, Department of Mathematics, National University of Singapore

Zhiming Chen, Professor

Computational methods for the nonlinear Schroedinger equation with low regulaity potential and nonlinearity

10:00-11:00 October 13(Monday), N208

In this talk, we begin with the nonlinear Schroedinger equation  (NLSE) with different low regularity potentials and nonlinearities arising from modeling and simulation for quantum physics and chemistry,  nonlinear/quantum optics, and quantum information and computation, etc. Optimal error bounds for time-splitting methods and exponential wave integrators are established for the NSLE under the proper regularity  assumption on its solution determined by the low regularity potential and nonlinearity. Then we propose a novel symmetric and explicit Gautschi-type exponential wave integrator (sEWI) for the NLSE with low regularity potential and nonlinearity, and establish its optimal error estimates under various regularity assumptions on potential and nonlinearity. Extensions to the NLSE with singular potentials and nonlinearities are presented. Finally, extensions to other dispersive PDEs with low regularity potential and nonlinearity are discussed. 

This talk is based on joint works with Remi Carles, Yue Feng, Bo Lin, Ying Ma, Chunmei Su, Qinglin Tang and Chushan Wang.