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

共 50 条

[41] Orbital stability of periodic waves for the nonlinear Schrodinger equation
Gallay, Thierry
Haragus, Mariana
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2007, 19 (04) : 825 - 865
[42] Periodic and quasi-periodic solutions of a derivative nonlinear Schrodinger equation
Liu, Jie
APPLICABLE ANALYSIS, 2016, 95 (04) : 801 - 825
[43] Quasilinear theory for the nonlinear Schrodinger equation with periodic coefficients
Medvedev, SB
Fedoruk, MP
JETP LETTERS, 2004, 79 (01) : 16 - 20
[44] Nonlinear perturbations of a periodic Schrodinger equation with supercritical growth
Figueiredo, Giovany M.
Miyagaki, Olimpio H.
Moreira, Sandra Im.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2015, 66 (05): : 2379 - 2394
[45] On the construction of almost periodic solutions for a nonlinear Schrodinger equation
Pöschel, J
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2002, 22 : 1537 - 1549
[46] Periodic and Bloch Solutions to a Magnetic Nonlinear Schrodinger Equation
Clapp, Monica
Iturriaga, Renato
Szulkin, Andrzej
ADVANCED NONLINEAR STUDIES, 2009, 9 (04) : 639 - 655
[47] Stability of small periodic waves for the nonlinear Schrodinger equation
Gallay, Thierry
Haragus, Mariana
JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 234 (02) : 544 - 581
[48] Rogue periodic waves of the focusing nonlinear Schrodinger equation
Chen, Jinbing
Pelinovsky, Dmitry E.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2018, 474 (2210):
[49] Remarks on some periodic solutions of the nonlinear Schrodinger equation
Grecu, D.
Visinescu, Anca
SIX INTERNATIONAL CONFERENCE OF THE BALKAN PHYSICAL UNION, 2007, 899 : 365 - +
[50] Quasi-periodic solutions in a nonlinear Schrodinger equation
Geng, Jiansheng
Yi, Yingfei
JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 233 (02) : 512 - 542

← 1 2 3 4 5 →