Geodesic
On a Solution of the Gross–Pitaevskii Equation for a Condensate Wave Function
Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 604-607 
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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     author = {V. P. Maslov and A. V. Churkin},
     title = {On a {Solution} of the {Gross{\textendash}Pitaevskii} {Equation} for a {Condensate} {Wave} {Function}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {604--607},
     year = {2005},
     volume = {78},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a9/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Gross E. P., “Hydrodynamics of a superfluid condensate”, J. Math. Phys. A, 4 (1963), 195–207 | DOI

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

[3] Lifshits E. M., Pitaevskii L. P., Statisticheskaya fizika. Ch. 2. Teoriya kondensirovannogo sostoyaniya veschestva, Nauka, M., 1978

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