On the Gross-Pitaevskii equation with strongly anisotropic confinement: Formal asymptotics and numerical experiments

Weizhu Bao; Peter A. Markowich; Christian Schmeiser; Rada M. Weishäupl

doi:10.1142/S0218202505000534

On the Gross-Pitaevskii equation with strongly anisotropic confinement: Formal asymptotics and numerical experiments

Weizhu Bao^*, Peter A. Markowich, Christian Schmeiser, Rada M. Weishäupl

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

The three-dimensional (3D) Gross-Pitaevskii equation with strongly anisotropic confining potential is analyzed. The formal limit as the ratio of the frequencies ε tends to zero provides a denumerable system of two-dimensional Gross-Pitaevskii equations, strongly coupled through the cubic nonlinearities. To numerically solve the asymptotic approximation only a finite number of limiting equations is considered. Finally, the approximation error for a fixed number of equations is compared for different ε tending to zero. On the other hand, the approximation error for an increasing number of terms in the approximation is observed.

Original language	English (US)
Pages (from-to)	767-782
Number of pages	16
Journal	Mathematical Models and Methods in Applied Sciences
Volume	15
Issue number	5
DOIs	https://doi.org/10.1142/S0218202505000534
State	Published - May 2005
Externally published	Yes

Keywords

Approximation error
Fourier expansion
Gross-Pitaevskii equation
Spectral decomposition
Time splitting-spectral techniques

ASJC Scopus subject areas

Modeling and Simulation
Applied Mathematics

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title = "On the Gross-Pitaevskii equation with strongly anisotropic confinement: Formal asymptotics and numerical experiments",

abstract = "The three-dimensional (3D) Gross-Pitaevskii equation with strongly anisotropic confining potential is analyzed. The formal limit as the ratio of the frequencies ε tends to zero provides a denumerable system of two-dimensional Gross-Pitaevskii equations, strongly coupled through the cubic nonlinearities. To numerically solve the asymptotic approximation only a finite number of limiting equations is considered. Finally, the approximation error for a fixed number of equations is compared for different ε tending to zero. On the other hand, the approximation error for an increasing number of terms in the approximation is observed.",

keywords = "Approximation error, Fourier expansion, Gross-Pitaevskii equation, Spectral decomposition, Time splitting-spectral techniques",

author = "Weizhu Bao and Markowich, {Peter A.} and Christian Schmeiser and Weish{\"a}upl, {Rada M.}",

year = "2005",

month = may,

doi = "10.1142/S0218202505000534",

language = "English (US)",

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pages = "767--782",

journal = "Mathematical Models and Methods in Applied Sciences",

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T1 - On the Gross-Pitaevskii equation with strongly anisotropic confinement

T2 - Formal asymptotics and numerical experiments

AU - Bao, Weizhu

AU - Markowich, Peter A.

AU - Schmeiser, Christian

AU - Weishäupl, Rada M.

PY - 2005/5

Y1 - 2005/5

N2 - The three-dimensional (3D) Gross-Pitaevskii equation with strongly anisotropic confining potential is analyzed. The formal limit as the ratio of the frequencies ε tends to zero provides a denumerable system of two-dimensional Gross-Pitaevskii equations, strongly coupled through the cubic nonlinearities. To numerically solve the asymptotic approximation only a finite number of limiting equations is considered. Finally, the approximation error for a fixed number of equations is compared for different ε tending to zero. On the other hand, the approximation error for an increasing number of terms in the approximation is observed.

AB - The three-dimensional (3D) Gross-Pitaevskii equation with strongly anisotropic confining potential is analyzed. The formal limit as the ratio of the frequencies ε tends to zero provides a denumerable system of two-dimensional Gross-Pitaevskii equations, strongly coupled through the cubic nonlinearities. To numerically solve the asymptotic approximation only a finite number of limiting equations is considered. Finally, the approximation error for a fixed number of equations is compared for different ε tending to zero. On the other hand, the approximation error for an increasing number of terms in the approximation is observed.

KW - Approximation error

KW - Fourier expansion

KW - Gross-Pitaevskii equation

KW - Spectral decomposition

KW - Time splitting-spectral techniques

UR - http://www.scopus.com/inward/record.url?scp=18644371907&partnerID=8YFLogxK

U2 - 10.1142/S0218202505000534

DO - 10.1142/S0218202505000534

M3 - Article

AN - SCOPUS:18644371907

SN - 0218-2025

VL - 15

SP - 767

EP - 782

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

IS - 5

ER -

On the Gross-Pitaevskii equation with strongly anisotropic confinement: Formal asymptotics and numerical experiments

Abstract

Keywords

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