Numerical Simulations of Soliton Collisions in Two-component Bose-Einstein Condensates

• Main Authors: Yung-Hsien Lu, 呂勇賢
• Other Authors: 陳宜良
• Format: Others
• Language: en_US
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/56965243178143629656

碩士 === 國立臺灣大學 === 數學研究所 === 103 === We investigate interaction of bright solitons for two-component Bose-Einstein condensates (BECs) in one and two dimensions numerically (1D, 2D). The numerical methods we adopt are: (1) Gradient flow with discrete normalization (GFDN) method for computing the profile function of solitons in 2D. We use backward Euler sine pseudospectral (BESP) method to discretize it. The algorithm is constructed by Chern and Bao [2]. (2) Timesplitting sine pseudospectral (TSSP) method for computing the evolution of wave functions. The algorithm is construct by Bao [1]. We discuss the change of velocities and shapes of the wave packets during and after the interactions between them. It is found that (1) In 1D, soliton collisions are like elastic collisions under strong repulsive interactions. When the interactions are attractive and strong enough, the wave packets may split into two or more parts after collisions. (2) In 2D, wave packets spread out after collisions when the interactions are repulsive or weak attractive. The wave functions blow up during interactions when the attractive interactions are strong enough.