KIT

Abstract

In this talk, I will review our recent work on quantized vortex stability and dynamics in Ginzburg-Landau-Schroedinger and nonlinear wave equation for modeling superfluidity and superconductivity as well as nonlinear optics. The reduced dynamic laws for quantized vortex interaction are reviewed and solved analytically in several cases. Direct numerical simulation results for Ginzburg-Landau-Schroedinger and nonlinear wave equations are reported for quantized vortex dynamics and they are compared with those from the reduced dynamics laws.

References:

[1] Y. Zhang, W. Bao and Q. Du, The Dynamics and Interaction of Quantized Vortices in Ginzburg-Landau-Schroedinger equations, SIAM J. Appl. Math., Vol. 67, No. 6, pp. 1740-1775, 2007

[2] Y. Zhang, W. Bao and Q. Du, Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrodinger equation, Eur. J. Appl. Math., Vol. 18, pp. 607-630, 2007.

[3] W. Bao, Q. Du and Y. Zhang, Dynamics of rotating Bose-Einstein condensates and their efficient and accurate numericalcomputation, SIAM J. Appl. Math., Vol. 66 , No. 3, pp. 758-786, 2006.