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

页码：539 / 564

页数：26

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