Applied Mathematics Seminar
Fri, 22 April, 2016
6:00pm
Speaker: Yongyong Cai, Purdue University Mathematics Department
Title: Numerical methods for nonlinear Schroedinger equations and applications
Abstract:
Nonlinear Schroedinger equation (NLSE) is a widely used model in different subjects, such as quantum mechanics, condensed matter physics, nonlinear optics etc. In this talk, we will focus on NLSE with applications in Bose-Einstein condensation (BEC), where NLSE is also known as the Gross-Pitaevskii equation. We will consider the GPE with dipole-dipole interaction modeling degenerate dipolar quantum gas. The two important issues in the study of BEC, the ground
states and the dynamics, will be discussed. In the second part, a nonlinear Schroedinger equation with wave operator (NLSW) will be discussed. The NLSW is NLSE perturbed by the wave operator with strength described by a dimensionless parameter, which causes high oscillation in time and brings significant difficulties in designing and analyzing numerical methods with uniform accuracy. We will propose a uniformly accurate method for NLSW and apply it to Kleign-Gordon equation in the nonrelativistic limit regime.
states and the dynamics, will be discussed. In the second part, a nonlinear Schroedinger equation with wave operator (NLSW) will be discussed. The NLSW is NLSE perturbed by the wave operator with strength described by a dimensionless parameter, which causes high oscillation in time and brings significant difficulties in designing and analyzing numerical methods with uniform accuracy. We will propose a uniformly accurate method for NLSW and apply it to Kleign-Gordon equation in the nonrelativistic limit regime.