On the Gross-Pitaevskii equation with strongly anisotropic confinement: Formal asymptotics and numerical experiments
Bao, W. Markowich, P.A. Schmeiser, C. Weishäupl, R.M.
Markowich, P.A.
Schmeiser, C.
Weishäupl, R.M.
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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. © World Scientific Publishing Company.
Keywords
Approximation error, Fourier expansion, Gross-Pitaevskii equation, Spectral decomposition, Time splitting-spectral techniques
Source Title
Mathematical Models and Methods in Applied Sciences
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Series/Report No.
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Date
2005-05
DOI
10.1142/S0218202505000534
Type
Article