A Hermite pseudo-spectral method for solving systems of Gross-Pitaevskii equations

Rada M. Weishäupl; Christian Schmeiser; Peter A. Markowich; Juan Pablo Borgna

doi:10.4310/cms.2007.v5.n2.a4

A Hermite pseudo-spectral method for solving systems of Gross-Pitaevskii equations

Rada M. Weishäupl^*, Christian Schmeiser, Peter A. Markowich, Juan Pablo Borgna

^*Corresponding author for this work

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

4 Scopus citations

Abstract

We propose and analyze discretization methods for solving finite systems of nonlinearly coupled Schrödinger equations, which arise as an asymptotic limit of the three-dimensional Gross-Pitaevskii equation with strongly anisotropic potential. A pseudo-spectral method with Hermite basis functions combined with a Crank-Nicolson type method is introduced. Numerical experiments are presented, including a comparison with an alternative discretization approach.

Original language	English (US)
Pages (from-to)	299-312
Number of pages	14
Journal	COMMUNICATIONS IN MATHEMATICAL SCIENCES
Volume	5
Issue number	2
DOIs	https://doi.org/10.4310/cms.2007.v5.n2.a4
State	Published - 2007
Externally published	Yes

Keywords

Fourier expansion
Gross-Pitaevskii equation
Hermite polynomials
Spectral decomposition

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.4310/cms.2007.v5.n2.a4

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title = "A Hermite pseudo-spectral method for solving systems of Gross-Pitaevskii equations",

abstract = "We propose and analyze discretization methods for solving finite systems of nonlinearly coupled Schr{\"o}dinger equations, which arise as an asymptotic limit of the three-dimensional Gross-Pitaevskii equation with strongly anisotropic potential. A pseudo-spectral method with Hermite basis functions combined with a Crank-Nicolson type method is introduced. Numerical experiments are presented, including a comparison with an alternative discretization approach.",

keywords = "Fourier expansion, Gross-Pitaevskii equation, Hermite polynomials, Spectral decomposition",

author = "Weish{\"a}upl, {Rada M.} and Christian Schmeiser and Markowich, {Peter A.} and Borgna, {Juan Pablo}",

year = "2007",

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AU - Weishäupl, Rada M.

AU - Schmeiser, Christian

AU - Markowich, Peter A.

AU - Borgna, Juan Pablo

PY - 2007

Y1 - 2007

N2 - We propose and analyze discretization methods for solving finite systems of nonlinearly coupled Schrödinger equations, which arise as an asymptotic limit of the three-dimensional Gross-Pitaevskii equation with strongly anisotropic potential. A pseudo-spectral method with Hermite basis functions combined with a Crank-Nicolson type method is introduced. Numerical experiments are presented, including a comparison with an alternative discretization approach.

AB - We propose and analyze discretization methods for solving finite systems of nonlinearly coupled Schrödinger equations, which arise as an asymptotic limit of the three-dimensional Gross-Pitaevskii equation with strongly anisotropic potential. A pseudo-spectral method with Hermite basis functions combined with a Crank-Nicolson type method is introduced. Numerical experiments are presented, including a comparison with an alternative discretization approach.

KW - Fourier expansion

KW - Gross-Pitaevskii equation

KW - Hermite polynomials

KW - Spectral decomposition

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U2 - 10.4310/cms.2007.v5.n2.a4

DO - 10.4310/cms.2007.v5.n2.a4

M3 - Article

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VL - 5

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JO - COMMUNICATIONS IN MATHEMATICAL SCIENCES

JF - COMMUNICATIONS IN MATHEMATICAL SCIENCES

IS - 2

ER -

A Hermite pseudo-spectral method for solving systems of Gross-Pitaevskii equations

Abstract

Keywords

ASJC Scopus subject areas

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