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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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/

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[2] Pitaevskii L. P., “Vikhrevye niti v neidealnom boze-gaze”, ZhETF, 40:2 (1961), 646–651

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[4] Bongs K., Sengstock K., “Physics with Coherent Matter Waves”, Report on Progress in Physics. A, 67 (2004), 907–963 | DOI