ON THE GROSS–PITAEVSKII EQUATION WITH STRONGLY ANISOTROPIC CONFINEMENT: FORMAL ASYMPTOTICS AND NUMERICAL EXPERIMENTS-Reference-Cited by-同舟云学术

ON THE GROSS–PITAEVSKII EQUATION WITH STRONGLY ANISOTROPIC CONFINEMENT: FORMAL ASYMPTOTICS AND NUMERICAL EXPERIMENTS

Published:2005-05 Issue:05 Volume:15 Page:767-782
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

BAO WEIZHU¹,MARKOWICH PETER A.²,SCHMEISER CHRISTIAN³⁴,WEISHÄUPL RADA M.²

Affiliation:

1. Department of Computational Science, National University of Singapore, Singapore 117543, Singapore

2. Institut für Mathematik, Universität Wien, Nordbergstr. 15, 1090 Vienna, Austria

3. Institut für Analysis und Scientific Computing, TU Wien, Wiedner Hauptstr. 8-10, 1040 Vienna, Austria

4. Johann Radon Institute for Computational and Applied Mathematics, Altenbergstr. 69, 4040 Linz, Austria

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202505000534

Reference8 articles.

1. Ground States and Dynamics of Multicomponent Bose--Einstein Condensates

2. Numerical solution of the Gross–Pitaevskii equation for Bose–Einstein condensation

3. Remarks on Nonlinear Schrödinger Equations with Harmonic Potential

4. The global Cauchy problem for the non linear Schrödinger equation revisited

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