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We compare the exact evolution of an expanding three-dimensionalBose-Einstein condensate with that obtained from the effective scaling approachintroduced in D. Gu\'ery-Odelin [Phys. Rev. A 66, 033613 (2002)]. Thisapproach, which consists in looking for self-similar solutions to be satisfiedon average, is tested here in different geometries and configurations. We findthat, in case of almost isotropic traps, the effective scaling reproduces withhigh accuracy the exact evolution dictated by the Gross-Pitaevskii equation forarbitrary values of the interactions, in agreement with the proof-of-concept ofM. Modugno, G. Pagnini, and M. A. Valle-Basagoiti [Phys. Rev. A 97, 043604(2018)]. Conversely, it is shown that the hypothesis of universalself-similarity breaks down in case of strong anisotropies and trappedgeometries.

Effective self-similar expansion of a Bose-Einstein condensate: Free space vs confined geometries