Geodesic
On a Solution of the Gross--Pitaevskii Equation for a Condensate Wave Function
Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 604-607

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In this paper, we consider an approximate solution of the Gross–Pitaevskii equation in the one-dimensional case in the form of the eigenfunction of the ground state of the harmonic oscillator. A numerical experiment shows that the approximate solution obtained satisfies, with high accuracy, the Gross–Pitaevskii equation for the interatomic-interaction potential in the form of the superposition of Gaussian functions. 
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     author = {V. P. Maslov and A. V. Churkin},
     title = {On a {Solution} of the {Gross--Pitaevskii} {Equation} for a {Condensate} {Wave} {Function}},
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V. P. Maslov; A. V. Churkin. On a Solution of the Gross--Pitaevskii Equation for a Condensate Wave Function. Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 604-607. http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a9/