NUMERICAL SIMULATION OF THE NONLINEAR SCHRODINGER EQUATION WITH MULTIDIMENSIONAL PERIODIC POTENTIALS

被引：15
|
作者：
Huang, Zhongyi [1 ]
Jin, Shi [1 ,2 ]
Markowich, Peter A. [3 ,4 ]
Sparber, Christof [4 ,5 ]
机构：
[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
[2] Univ Wisconsin, Dept Math, Madison, WI 53706 USA
[3] Univ Vienna, Fac Math, A-1090 Vienna, Austria
[4] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 0WA, England
[5] Wolfgang Pauli Inst Vienna, A-1090 Vienna, Austria
来源：
MULTISCALE MODELING & SIMULATION | 2008年 / 7卷 / 02期
关键词：
nonlinear Schrodinger equation; Bloch decomposition; time-splitting spectral method; Bose-Einstein condensates; Thomas-Fermi approximation; lattice potential;
D O I：
10.1137/070699433
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
By extending the Bloch-decomposition-based time-splitting spectral method we introduced earlier, we conduct numerical simulations of the dynamics of nonlinear Schrodinger equations subject to periodic and con. ning potentials. We consider this system as a two-scale asymptotic problem with different scalings of the nonlinearity. In particular we discuss (nonlinear) mass transfer between different Bloch bands and also present three-dimensional simulations for lattice Bose-Einstein condensates in the super fluid regime.
引用
收藏
页码：539 / 564
页数：26
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